I think you are talking about a sago palm. Sago palms arent actually palm trees, or related to palms, they are cycads. Im not sure what caused the mother plant's fronds to yellow, but it might not be dead. Just leave the plant as is and it will do its own thing. If there are a lot of babies then you can remove a few of them once they are a little older, but I would leave them for now.

Good luck!
-Alex