Is it legal for a parent to give their children money for 24/7 care as the state wants all money to be accounted for in case of nursing home?

If it’s the situation that your parent has already moved into a facility, is a “Medicaid Pending” resident and applied for Medicaid so you as the dpoa are in the document gathering stage and you’ve realized mom has done “gifting”, I’d suggest you ASAP set up an appointment with a elder law atty. Imo unless the $ was one time low value item (like an old car, I dealt with this for my mom) or perhaps small amounts fewer than a dz times over 5 years (my bil dealt with this with my mil), it’s not ever a DIY project. Dealing with after the fact discovery is pretty sticky. Plus your states Medicaid may have narrow timeframes & specifics needed for reporting that’s easier for an experienced atty to keep up with. If mom gave $ to an errant sibling or grandkid, it will be especially messy. You can let the atty handle whatever financial issues arise and they shepherd your parents application.

Set up a caregiving contract using a lawyer. Mom may pay her kids for caregiving, taxes withheld, etc. She cannot simply "give them money".