if an elderly person adds children to his accounts (not just signers, actual owners), and the child moves money out of that account and opens a new one, does the State / Government have access to that money that has been moved, in order to pay for nursing home care?
If you are Dad's DPOA, I'd suggest you go to the bank (dress nice, have your DPOA, ID & if you have a passport take that too) and speak with a bank officer (not a teller), and clearly go over just what the banking situation is for every account so that you know what the ownership situation is.
Is your ? about your concern on future issues with Medicaid? If you anticipate that Dad is going to need to apply for NH Medicaid and funds have been taken out by the kids within the past 5 years, it likely will show up for the Medicaid application review.
For my mom, Medicaid required 3 years and 6 months of all financials and did a 5 year review on real property (land, homes, car).I had to go to the bank and get a officer to do a letter as to the disposition of each and every account, CD, Tbill closed too within that period. Fortunately as accounts closed or CD's expired, the proceeds all went into mom's main checking account, so it was clear that all her funds went to her and were spent by her with no transfers or other funny stuff.
Now Medicaid cannot access your banking, BUT what they can do is not pay the NH for your parents care. If your parent gets a transfer penalty, the NH gets the letter too from Medicaid. The NH can have a claw-back of Medicaid payments and they will not be happy. The NH fully expects to get paid and will go after whomever signed mom into the NH or is the DPOA for the payment due. If mom gave your worthless brother 10K & he won't pay, then you or others in the family will have to cover the transfer penalty if you want mom to stay in the NH. Otherwise decide which room in your house mom will live in till the transfer penalty period is over. Realize the NH bill will still be there during this period of time and they can turn it over to debt collection if they want too and it is worth their doing. Transfer penalties cannot just be ignored and are sticky to deal with and usually you need to hire an elder law attorney to work the appeal.
Honestly, if there were simple ways to make inconvenient assets disappear off the books everyone would be doing it. There aren't any. Forget it.
And I know it is a sore subject, but I have yet to hear a cogent argument that explains why an elderly person should not pay for his or her accommodation if he or she does in fact have the money to do so. Concealing or wilfully divesting assets is not wrong because it amounts to tax evasion, it is wrong because it amounts to a fraudulent benefit claim. Desist.
If you have co-mingled money, you need to talk to an adviser to see if there is a way it can be undone. If the money was only deposited by the parent, then no problem. It is the parents' money.