There is no really sheap way.
The best I have found is Business Mail, but that only works if you live in Santiago, Santo Domingo or Puerto Plata.
You mail the package to an address in Miami and they take it from there.
Costs are under $3.00 a pound. plus aduana and handling. A whole lot less than FedEx or anyone else.
Your family here would have to join up with Business Mail and get a code for mail and packages. It would work like this:
Pedro Perez (S-1234)
xxxx N W 98 Ave
Suite f
Miami, FL 33333
That is nowhere near the real address but it serves as a model
See if that would work for your folks.
HB