I was wondering if the box i have is to small for princess and all the babies and had though about moving them into a huge rabbit cage we have?The all seem comfortable in the box.
I did just what you're thinking, I turned a large bunny cage into the kittening cage and covered the top with thick towels to keep the draft down. I think it worked really well in that it was large enough for me to put a scratching post in one corner, and a small litter pan in another when they were ready to start learning how to use those, and still have the other side of the cage to curl up and nurse/sleep.
With my moms with young litters they are kept in extra large dog crates with a rubbermaid container with a whole cut in it big enough for mom to get and kittens to get out once they are mobile enough too. It cuts out the chance of young kittens getting chilled and gives mom privacy.
As the kittens grow, you need more room for both mom/kittens, so it sounds like it worked well. I used a sheet over my large kitten cage to keep out the drafts.