where to keep new second dog at night and while gone

I would keep his crate in your bedroom to help him feel part of the family.  I'd keep him crated, even at night, until he's settled in and has learned the routine.  He may have done well in the foster home (assuming this, since he's from a rescue) but that might not translate to your home until he's been there for a few weeks.  I don't think I would worry too much about the frustration factor. Three of our four dogs are crated at night.  None of the crated dogs seem to feel any frustration that they are crated and one is not.  All of them sleep in our bedroom.  Yes, it's a dog house around here. lol

 The only reason why don't want to keep the crate in our room is because this dog tends to go in his crate for naps and when stressed.  He will not have unsupervised access to our upstairs during the day.

 Have these dogs met yet?  If not, I would introduce them on neutral territory, not at your home, then bring them home together. Once there, if you need to crate him until you're sure, then do.

 Yes, they've met twice.  Once outside only, then outside and in.  They played a bit roughly, but no one harmed each other.  I am definitely going to be crating the new guy until I'm 100% sure they won't hurt each other.  I'm just not sure where to keep the crate. 

To be honest?  Your answer lies in TWO crates.  Being part of the "pack" at night is HUGE to a dog.  That "sleep smell" is a big deal to them in bonding and being a part of everything.

But you don't want to schlep a crate back and forth so honestly a 2d crate is likely your answer unless you can completely dog-proof a separate room (and even then I'd rather use a wire crate so they can see/hear each other).

I have a soft-sided crate I use this way sometimes -- put the sturdier crate downstairs for day, and just have a soft-sided one for at night in your bedroom until you feel comfortable having him loose (which is usually several months before they're "trusty";) -- but we love a soft-sided crate as a 2d because it comes in so handy when we travel.

My dog set up is similar to what yours would be - Wendy is crated in the same room that Pirate is confined in. I've never had a problem with it :)

 Unfortunately, I can't run out and buy another crate right now.  We haven't officially adopted this guy yet.  We're just giving it a trial run this weekend to see how the 2 dogs get along after a few hours.  I've already spent quite a bit of cash of basic supplies, a huge plastic crate, a vet visit, etc...   Until I know for sure that we're adopting him, I can't spend any more.  I've always kept any new dog in our room in a crate until they were trustworthy enough to pick where they wanted to sleep.  I don't like the idea of locking him in a crate downstairs where I can't hear him.  Ideally, he will sleep in my daughter's room, if we keep him.  I just can't lug the crate up and down the stairs.

 I may just keep the crate up in daughter's room.  Put him in it at night and while gone during the day. I'll let my current dog do her usual routine.  During the day, while I'm home, hopefully he can find another "safe spot" to lay when he wants to nap.