How can I get my cat to stop pooping on my kid's bed?

Your cat is not jealous of the new child. Your cat is stressed out.

Most cats like calm, quiet, routine, and for their territory to not be disrupted. Unfortunately, with a new baby, all those things tend to go out the window.

It seems to be a rather common reaction when new parents bring their child home, for their cat to start eliminating in locations where their child's smell will be particularly concentrated. It's almost certainly the case it's because the cat is feeling stressed because some new being has come into its territory, and so it's trying to re-establish its territory.

Spread your cat's scent.

Hopefully, if you spread your cat's scent around, your cat will no longer feel the need to inappropriately eliminate. Move things your cat frequently uses into the child's room, such as blankets or beds. Add cat furniture to the room, so the cat has its own places to go in that room. Try to put your cat's smell as close to the baby's bed as you can, so the cat will feel like it's marked this area, but of course still be careful to not put anything in the baby's reach that might be a danger. I'm thinking perhaps a cat scratcher beside the bed might be ideal.

You might also want to add another litterbox close to the baby's room, so the cat will have an appropriate place to go that's more convenient.