If I were to get a divorce, am I still financially responsible for my MILs care?

I think you are conflating some issues.

You (as in you and your husband) are not responsible for paying for MILs care. SHE is.

If MIL gifted you all money and you need to pay it back, that's something that you work out (the question is, is this "marital debt") with the divorce mediator or lawyer. I highly recommend mediation

The divorce was a long time coming. Taking care of my MIL has just heightened the problems that have existed between us for years.

Was the money gifted to you?

The person she gifted the money to is the one who this burden should fall on.

Are you thinking of divorcing your spouse just to get out of paying for MIL’s care? Before I did that, I would consult with any attorney who specializes in Medicaid and/or Elder Law to see what options you have. Paying for a divorce will cost you big bucks too.