Will all of the funds in a joint account need to be depleted with the exception of 2K when we apply for Medicaid?

Some (but not all) prepaid funeral expenses are allowed. Talk to an Elder Care Attorney During the spend down, this is an authorized use of the money.

There are two types of Medicaid; community and chronic. The amount of money you are allowed to keep are different for each one and different in each state. There are other state specific rules that protect a community spouse from impoverishment. An elder care lawyer who specializes in Medicaid would be a good person to consult. If that is too expensive, try the Administration on Aging. It's important to know the rules because if you spend or move her money improperly and then she needs to qualify for chronic Medicaid, you might have to pay for care yourself for a time before Medicaid will start.

What is the source of the money in the account? If it was from a lump sum payment (such a tax refund), it might be exempt for a period of time.

In Texas, pre paid funeral expenses are exempt as are some other expenses for your Mom. You can check with a Medicaid expert that works for the state and get free advise as opposed to paying a lawyer.