Would Medicaid deny me if I take out money every month for entertainment for my Dad?

Take money out of what? If your father is in a nursing home on Medicaid, he will get a small personal needs allowance each month and the nursing home will take the rest. The personal needs allowance can be used for the things you mention, but it's very minimal.

Medicaid is not your problem. You signed a contract with the nursing home and if you do not pay the full amount, they will evict him. If you are POA, the nursing home will sue you and win. Please read the contract.