I understand -- and if crating won't work because of prior issues that's fine.
However -- I'd also suggest that if she's having UTI issues as you mentioned above, this can also impact things. some dogs quit drinking when they have a UTI because it burns to pee. Their urine gets really dark, stinky and sometimes it can be hard for them TO void (so they'll squat, try, ... go a few steps, try again ... etc.)
However, other dogs are a bit more clever and they will drink MORE when they are uncomfortable. They learn that the more they drink the less it burns when they void ... so they may drink more in an attempt to lessen the pain and then can't hold it well.
99.999999% of the time dogs are seriously a product of their background.
Fear is possible but usually you'd know that when you came home. However -- since you're gone most of the time and can't "see" it's entirely possible that she's hearing a sound (could literally be even the sound of a particular make of car, or someone passing by -- even someone knocking at the door or making noise outside) that may unnerve her -- THAT can cause them to leak or lose control for sure.
But she's going to the linoleum ... that means to me that's what she's done in the past. And either it's a particular environmental trigger or something physical that causes the wetting.
Some folks treat to housetrain -- I don't. It's too easy to confuse them.
Right now you are in what is known as the "honeymoon" period. She knows she's fortunate -- she's likely gone from a situation where there was little positive (and likely little good structure and care) to a situation where she's got a human who CARES. so she's likely trying hard to do what you want.
But when a dog is that age it can take aeons to really begin to figure out what's up with them. And it can be THE oddest things that can trigger a memory or a fear.
True story: One time several years ago my husband and I adopted a little pup (she was only 4 1/2 months old) who had been horribly abused. Her abuser had broken her back with a broom and she couldn't walk.
She thrived with us and did very well ... but unfortunately her injuries were too severe and a blood clot/stroke took her in less than 3 months. (But oh she knew love and joy with us!)
BUT ... altho she'd been horribly misused there was no hand-shyness or such to indicate the abuse. However -- periodically she would just get TERRIFIED and fall to pieces ... and then just as suddenly she was FINE. It would even occasionally happen in the *car*. And that's how I finally figured out the key.
She was TERRIFIED when she heard a Dodge Durango!!!
We had neighbors who had a Dodge Durango and apparently her reaction in the house was when she heard their car (my husband actually caught this happening several times once we figured out the car was the trigger to the fear).
But when we were in the car, she could be sound asleep and if we suddenly pulled along side a Durango on the interstate she was instantly awake and trembling.
I eventually called the police dept in the town where she came from and yep -- the idiot who had abused her HAD A DURANGO.
Now that sounds completely weird -- but apparently different makes of vehicles sound differently. And she would get scared when HE came home. But when the car went away she was 'safe"
Your little girl may have a sharp fear of some particular thing. My car story about Polly was only one small example. It can be the smell of a particular type of aftershave/perfume, or it can be particular sounds (keep track in a notebook and see if you can pin down a particular day/time that she has accidents -- like trash day, or the day the bug spray guy is around outside, etc.).
OR ... as likely as 'fear' -- she could have had a bad experience as simply hate certain things in the same way.
You've only had her 3 weeks -- and honestly, taking an older dog with "issues" -- it will take you MONTHS to sort it all out.
And when I say "bond" -- she obviously knows she's got a good deal going on and she likes you. But **trust** takes a long time to build. For her to fully trust you and know you are going to really protect her ... and for you to trust her and know what you can reasonably expect from her. That type of bond takes longer but it is SOOO rewarding.
In my many years of loving dogs, I've had many many senior ones. And I've adopted a good share very late in life. I have always found that to be a particularly rewarding experience.
The peke you see in my signature has only been with us 4 years. She wasn't horribly abused -- just neglected. But when she first came to us she was a mass of obsessive petit mal seizures. She literally lived in a near-seizure state ALL the time. She wandered thru a fog of air-licking and obsessions and virtually didn't hear anyone call her nor was she able to relate to anyone very much.
Once we got that treated (acupuncture and Chinese herbals -- she's never even had to be on harsh drugs) she has been a different dog. At first she wanted nothing to do with being held, nor cuddling a human. Never wanted to be on the furniture nor to be up in your arms.
Took a long time but she's now a real cuddle bunny and really **enjoys** being held. She is finally able to derive true comfort from us. Bringing a dog into a healthy state of joy is a really neat thing.
This may sound odd -- but even at her advanced age, the BEST thing you could possibly do is enroll her in a basic obedience class. Yep -- even as a senior.
Don't just take a class in a local pet store ... find a good one that uses positive reinforcment. But it will train *you* as much as her. But it will give you good experience in how to 'read' her and understand her better, as well as give you better tools to cope and train her.
Old dogs in obedience class are a riot. They catch on quicker than pups. Pups are SOOOO busy chasing leaves, being completely rowdy and all over the place ... and the older dog tends to focus far far better. And suddenly you have an older dog doing obedience RINGS around the youngsters.
It can build incredible confidence -- it's a really good thing for them socially (especially since you want to work on social situations) but it is just so awesome to see them blossom.
Good luck!! and welcome to you. There are a lot of really nice folks on here and some really superb trainers.