Wow, that is a hard situation to be in. It does sound as if Mom is prone to overreact but looking at this situation from a purely non-emotional one, I would have to agree with HoosierDaddy.
If OP was living somewhere else, he would be obligated to pay the rent and the landlord wouldn’t give one flying flip whether he actually lay his head there at night or not. It wouldn’t affect the obligation that he is to pay the monthly rent. Also, if the OP was living somewhere with a non-relative landlord, he would STILL be obligated to pay the last month’s rent regardless of wedding expenses, etc.
The situation here is tricky, though, because the landlord (and mother of the groom) is Mom and as a landlord, Mom wants the last month’s rent which is her right per their explicit or implicit agreement.
As for the Mother of the Groom issues previously experienced, that is a totally separate issue. She was being unreasonable and irrational about that and it certainly sheds light on her mental state. However, again, it has no bearing on the OP’s obligation to pay the last month’s rent.
Another reason why it’s not good for the borrower to be slave to the lender