No, the rules aren't the same, she's not three.
Let her ride. I don't see the big deal. She may have to understand that the 3 year old may need to ride more than her but otherwise, the stroller still needs to be pushed around.
Kids are fickle and we can't put our adult emotions and thoughts on them. Toddlers do what they do because....they just do. You can't really ask why. And those emotions can change within a few minutes.
You can prep a lot of things. Of course the bed was prepared but I gave birth on the floor on hands and knees. My water broke on the toilet so that wasn't too much of a big deal. I did get the carpet wet off of the chux pads but the midwives cleaned that up. I had no cleaning to do afterwards. My mom was there to put stuff in the dryer. We also had a lot of stuff we'd planned to toss anyways...old towels, old sheets, etc.
You may also want to remind dh that...
Congratulations on your pregnancy! I would just spend plenty of time on the MDC homebirth page. Look back through old posts and you'll get a ton of info. I also liked the book Ina May's Guide to Childbirth.
Sorry you're facing this! I don't have any advice. I don't know whether you'd be in a situation where you'd terminate. We all have different feelings about what we'd do personally. I would demand any more tests they can do.