Simple solution.
Every day, until the Marine is released, 2 747s will land at Mexico City airport and offload a full load of illegals. They will be forcibly removed from the aircraft and left on the hard standing, processing them is Mexico's problem. No luggage handlers will be needed, since they will have the clothes on their backs and whatever is in their pockets, nothing more.
If the Marine is not released after 3 weeks, all aid, both financial and military, to Mexico will be halted. Permanently. The immigrant flights will continue. All tourist traffic from the USA to Mexico will be barred.
After 6 weeks, Spec Ops will conduct a live fire exercise on Mexican soil.
Like I said - simple.