At this age it's best to contain them in a room - like a bedroom - and close the door so mama cannot drag them all over. It sounds like she is looking for a private place but can't decide, so a single room without much foot traffic might make mom feel more secure about her babies.
Can you put them in a closet in your bedroom and leave the door of the closet cracked? It sounds like mom is looking for some real peace and quiet. Do you have other children or just the new baby?
I think your cat is seriously looking for privacy. Do you have a really quiet, private place to put her with her kittens where your four-year-old will not disturb her? That sounds like the issue to me!
I feel your pain. When my kid were 4, 3 and a newborn, I paid a teenager to take the older two out for an hour or two every other day or so. I could take a nap and she would do fun things with them outside. I used the quarters from my husbands spare change jar to pay her. I actually had 3 teenagers I could call.
Yes, try that and close the bedroom door and keep your little one out. I would also put her food, water, and litter box in the bedroom so she only has to leave the closet briefly to meet her needs. I hope this will calm her down. Let us know if it solves the problem.