She's marking territory.
Now, when I say this *please* don't think I'm being snarky or mean -- but don't consider her housetrained *at all*. She may have a start on it, but a dog isn't house-trained until they really are. And an "accident" typically isn't an accident until they've been reliably trained for years (and then you start looking at the physical first).
However -- in the time you've had her, have you had her to the vet (I'm not going to assume the vet spayed her -- you could have had that done at a shelter)?? In honesty, the first thing to check would be to get a full urinalysis done on her. See -- you've only had her two months but she's 18 months old. She could have crystals or even a long term infection that might not immediately show up as a problem. Some dogs drink TONS and, in so doing, keep a long term infection almost invisible because they drink enough for the urine to not show dark.
1. So -- #1 is a vet visit with a full urinalysis - you can't rule out everything else unless you know **exactly** what's in the urine. Don't let them just do a strip test -- this isn't a waste even IF it's normal because it will give you a baseline on *her* if it is normal.
2. Make impossible for her to screw up. Yep -- I realize this is a "loaded statement". But it's honestly what you have to do in order to fully housetrain them.
That means you keep track of her every single instant so it is impossible for her to elminate improperly . The first time I'd let her drag a leash ALL the time and any time you aren't 100% focused on what **she** is doing you loop the leash handle over a belt and strap it on. This way if she's hunting for a place to go you will notice her sniffing or walking back and forth (or even squatting to pee or poop).
The instant you see her assume the position you say "Nuh uh ... not there -- **out** side!!" and walk FAST to the door you use and get her out to where you want her to go. If she's already started, pick her up in the towel you have looped over that belt and transport her. The best, most foolproof and easiest way to get her trained is literally catch her in the act (or almost) and get her outside. She'll get distracted but leave the towel on the ground and say "this goes **out** side!".
If she screws up and you're not quick enough. Put her in her crate for a minute, clean up the mess but take the paper towel outside and lay it down where you want her to go. Go back in and **thoroughly** clean the spot -- you may not smell anything but they will often return to a spot they've used before (and that's being *not* house-trained). Then go get her, on leash, and take her outside *then* and point to the mess and say "Outside! Put it here!" I will usually also point to the spot inside on the way out and simply say "No, not here". But literally show her that you have **moved** her waste to the appropriate spot. That makes the impression.
See dogs are completely situational and immediate -- even if you discover it **after** they simply will pick a spot either that they want to mark or that they have successfully used before and go there, rather than holding it. By "successful" I mean they have gone there uninterrrupted. Because if you come by later and say "Bad dog!" and point to a mess -- they literally think you're commenting on them (as in "I don't like you";) more than on their choice of spots.
They identify with their waste -- it is uniquely **them** -- the "where" of it was simply where it was convenient. It never occurs to them that your entire problem is ***where*** they put it. That's an entirely separate decision for them and they totally miss that inside/outside point.
3. **Asking** to go out -- you have to very deliberately train this. Most dogs will only give you a 'look' (and maybe not even that) and then will proceed to their own devices if you don't act immediately. This is one of the big reasons why you have to prevent them from screwing up. You have to literally be right there to make the point of where it needs to go and to *tell* you. They won't make a big investment of energy to tell you until they really understand that it is never, ever ok to go inside and you catch them every single time so they absolutely can't go without discovery.
One of my favorite suggestions is either to put a spring doorstop on the door you take them out, or hang a small bell on the door. As you get her to the door, stop just long enough to gently take her paw and bat the doorstop or bell to make a noise and say 'Outside!' and proceed out to the potty spot.
4. Some folks use treats as a reward for going outside. I never do because I've seen it be too easy for a dog to think "oh, if I pee/poop I'm gonna get a reward" and then do it inside expecting one.
5. Crating -- unfortunately you let her dictate to you that you won't crate her during the night. If you let them tell you they won't (by stirring up a stink and carrying on) then by letting her out you rewarded her hissy fit. If it were me I'd re-train the crate. Feed her in there, give her treats and a kong or something yummy in there when you want to leave her unattended while you do something else. Work up to longer time and to leaving but don't let her simply whine and carry on to be let out. But don't open the door when she's crying == **only** when she's quiet -- then reward the quiet by letting her out.
But during the night? You will have to devise some alternative method (unless you want to go back and simply let her have a fit for a few nights until you convince her that you won't let her out just because she "pitches a fit". (sorry, that's what we call it here)
But don't let her have free roam of any where. Keep her close enough to you so that you will wake up and take her out. I've seen people tie the leash to their waist again to know when she gets up and moves around. A cat bell tied to her collar will also make sound if you can wake up for that.
Just don't let her be loose during the night because a dog that won't hold it thru the night is not housetrained -- she needs to wake you up if she needs to go out (and then you need to address that as training and say "hold it longer" and make her wait a while longer before you take her out.) She was never taught as a puppy to hold it -- so most of this is habit -- but again, you can't let her have the freedom to go inappropriately during the night.
Essentially if she goes --- even one time -- successfully (i.e., without you right there to say "Not there! Outside!";) she has successfully broken training and taught herself that new spot is 'safe'. It has to be wrong all the time.
All this is what we dog lovers affectionately call "House-training 101" -- meaning back to the basics. When they've learned a whole host of bad habits, it's tough to change them.
6. NILIF -- this is one of my favorites and it honestly will help everything from housetraining to obedience -- but most of all it's training for the humans. NILIF is "Nothing In Life Is Free" -- and it's simply a method of dog training where you simply put her in a position to have to *ask* you for every single thing she wants. (You can Google that and come up with a ton of hits)
It's totally positive -- and it really doesn't take long to put it into effect -- you just plain teach them "sit" and when they begin to demand something you look down and say 'sit!' -- and they do and you give them that thing. Suddenly it almost becomes a game and they get all excited because wow -- communicating with this human just got EASY!! I "sit" and they're all happy with me and give me stuff!!
Food? Before you get your bowl you sit nicely without grumbling or barking for me to put your bowl down and *tell* you "OK". Even feeding her kibble one bit at a time for 3-4 kibbles and then putting down the bowl is often really effective.
Affection? Most people don't notice when the dog comes up and demands affection. Pawing your leg, jumping up next to you, or even the ever-popular "slide the head under the human's hand so they pet me automatically" -- nope. They need to come up to you and "sit" in front of you and THEN you bestow affection.
Why all the regimentation? It sounds like this takes all the fun out of dog ownership -- but it really doesn't. it simply defines boundaries and it cements that basic communication that the dog isn't running the show.
I really don't get into "dominance" and all the alpha stuff. This is just polite behavior for a dog and getting these boundaries straight makes it a whole lot easier to do everything -- including housetraining.
I didn't mean to over-instruct here, but when you feel like you've been stumbling around and something as frustrating as getting them to not make messes becomes almost 'normal' -- sometimes we all need a real plan to make the change.
BTW - we LOVE pictures on here and we'd love to see her!!