Haven't read the whole thread. I know what it's like to have a small home. Is there any way you could have a bed or mattress or something for the 4yo to sleep on near you? Maybe make it a rule for her to be on Daddy's side, to ensure safety for the new baby? If things were this bad, I'd be rearranging the house and getting rid of stuff to try to fit a mattress on the floor even near DH's side. Or getting a big bed for the other room and having DH sleep there (he did this a while b/c I had to sleep on my own, trying to sleep with great pain, and then DD got a bit used to it).
For what it's worth, DD is 3 and sleeps on her own. Sometimes she'll wake up with a nightmare (like last night, she woke crying but when I came in, already up from pregnancy insomnia and hunger, she said, was that just my dream? and cuddled and went back to sleep), or wanting water, even tho the water bottle is always right there, whatever, but the majority of nights she goes all night. I agree, it's important for kids to not be climbing in bed when there's a new baby there. Perhaps your 4yo will move past this phase soon, but if it keeps up, I'd move heaven and earth for better sleep, in whatever safe way I could. Good luck!