Not helpful as I don't have a cat but I honestly couldn't cope with that in normal times, if I was pregnant I couldn't cope at all.
Preparing for the arrival of your first is so special, I wouldn't want to bring my child into a house like that.
The PP who had to pick cat hair from her baby's skin folds 
I once moved in with a friend that had 2 house cats, they used the living room as a litter tray and the sofa was COVERED in their hair - I had to move out. It was vile.
Definitely keep them away from where the baby will sleep so you know that bit is clean.
But I loved my baby being on a blanket on the living room floor when she was a baby, we lay there together for hours, no way could I have done that on a hairy carpet.
I would keep them outside as much as possible as I wouldn't let the bully any where near my own cat. The worms and incontinence sound 🤢. You're going to be busy enough with your newborn without cleaning up after cats.
What I could train myself to cope with as an adult, I just wouldn't be able to accept for my baby.
I know that's probably not helpful, I think you're coping brilliantly!!
In have nothing against cats and LOVE getting to feed and fuss my neighbours beautiful cat - I even offered to have her while she has an extended break - but when pg and having babies, I couldn't cope with the mess, smell or extra demands on my time.