Your DH's dishonesty is the problem and I would probably be thinking very hard about the future.
You say you can't give details which does limit how people can help. But in terms of an arrangement - like hell would I work in a job I didn't want to, or give up time with my young child. Me, and my child, would be more of a priority than MIL. Tough.
The trouble is of course that because he lied until you were married, you are forced to fund because if he sends money he earns directly, you are forced to plug the gap.
Stop plugging the gap if it does not suit you and let him solve the problem. Drop the rope.
It's amazing how these kind of people, who are keen to drag others in to pay for their choices or debts, change their tune once their golden geese say no more.
Refuse to pick up that slack and I am pretty sure he'd rather not lose his own home than pay for MIL.
Where is she, can she work, are there other family members?