Does the nursing home have a right to keep Dad's pension along with social security, Medicaid, Medicare, etc?

Is dad in the NH for long term care (in which case the answer above is correct)or is he there for the short term as a rehab patient and is expected to return to the Assisted Living facility that you mention in your profile? Or is that still up in the air?

Yes they can. If dad is on Medicaid every bit of income he has needs to go towards his care, with the exception of $50.00 a month, in many areas for personal expenses. If is income is over $2,000.00 a month, then I imagine he is on a Medicaid waiver program where Medicaid picks up the expense that your dad cannot cover with his income. Nursing homes in my area start at about $8,000.00 a month so Medicaid would pay whatever the difference is between dad's incom and the Medicaid contracted rate.