can't sleep and pregnant kitty

I've been lying in bed since 8:30pm trying to sleep (very tired). My legs and feet have hurt all day and nothing has been helping - can't get comfy. I think I overstretched something in PT on Friday. :( I'm hoping a solid dose of my pain meds will knock me out soon.

Another thing that is keeping me up is thoughts of an abandoned(?) kitty that's made my backyard her home for the last week or so. I figured out yesterday that she is pregnant. She is a tiny Siamese. She'll let me get pretty close but won't let me touch her. She used to hop the 6' fence in my backyard but she is too big now to do so. She's been starving and I feel terrible that I didn't realize this sooner. I put some food, water, makeshift catbox (she is housetrained), and a "bed" on my back patio where she's been sleeping. She is responsive to my efforts in this respect.
It's been really hot here for the last few days, which doesn't help my worrying. She's clearly uncomfortable and the movements in her belly are big enough to think that she'll have the kittens soon. She's tried to get into my house, with success, yesterday. She appreciated the AC and seemed more comfortable physically. I left the door open for her today and she didn't want to leave. I have a cat already and keeping them apart is very difficult. Since I don't know anything about this cat, I don't want to get my cat sick. I thought the kitty had left my house but, hours later, I discovered she had been hiding under the couch (she camouflages well!). My friend and I shooed her out of the house out of concern for my own cat's comfort/health.
I've knocked on doors around the neighborhood to see if anyone is looking for her, but I've had no success. My concern is that she is from one of two neighbors that treat their animals poorly. The fact that she is pregnant is one indication that they've slacked off on good care.
Do I leave the cat outside and hope that she'll feel comfortable enough to have her kittens in the box I made (cardboard box with towel inside and "windows" cut into the sides for airflow and for lookout)? I can't catch her, so should I try trapping her and then isolate her in a room in my house? Do I call the county shelter to come pick her up? Neighbors I was able to speak with today, who live on either side of the "irresponsible" ones with lots of animals, said that they would not trust them to take care of a pregnant cat. The people who I think possibly own the cat, did not respond to my knock even though I could tell they were home. I did not look like a solicitor for sure. I don't want to come off as judgmental but I have a really sensitive heart when it comes to animals and mistreatment.
Oddly enough, I've been praying for strength to go into the local shelter to adopt an adult cat as a companion to my cat. Do I take this cat in? Is it wrong, especially if no one claims her? I'd get her neutered as soon as possible, and find good homes for the kittens (hopefully neuter them too beforehand). If I can catch her, I'd definitely bring her to the vet as soon as possible to check her health, see if she has a microchip, get her neutered, and update shots as needed. I don't think she's ever been to the vet (was just a kitten herself a year ago). I'd feel better letting her go if I know she can't have more kittens and is healthy.

Anyone with advice is welcome to respond. I am really torn on what to do.

Thanks. I'm going to try bed again now that I've gotten the kitty issue off my mind for now.

TTFN,
~e