Lets make a deal with Mexico

We have problems, they have problems. Our crime problems seem to be interwoven. Drugs that flow through Mexico cause a big chunk of that, but as long as there is demand, the drugs will be supplied.
We have a yuge number of people here illegally. Some are low class criminal scum, some are honest hard working souls who want nothing but a better life.
No matter what, we need to send the criminals back. I'd even go so far as to deposit them off the coast of Cancun, include an iron man swim in their regimen if they want to come back to the United States.
This isn't about Mexican criminals though. Wirecutter highlighted some of our problems, Heyjackass highlights still more. Two factors fuel that violence, a matriarchal society, and drugs.
My idea is this, We construct some decent affordable style housing in southern Mexico. Then we offer that housing to mothers of crime victims and delinquents from our inner city problem areas. Each family would be paid a reasonable monthly income and given free housing in Southern Mexico. Along with that, they would have the opportunity for close family to migrate there with them. These families would have a fresh start. If they then chose to dabble in drugs, the flow of poison would stay well south and the majority of Mexico would not need to endure the crime spree that goes with drug traffic.
In return we will keep illegals that have jobs, but they would be barred from medical and other community services. Make it a one for one deal, and it would benefit us all. Those transplants would receive a stipend just like they do now. Given the economy in Mexico, they would be able to live better there than here. Mexico would get income since they would need to spend their stipend.
I've had this idea in my head for several days. I know it needs a lot of refining, but it could work, and it would help both us and Mexico.