We are a 55+ co-op in Florida and in our by-laws it is stated that a 16 yrs can live here --He moved in a mother and a 6yrs old son. What is the recourse of this

Your question is a bit unclear. But if the by-laws state that all residents have to be over 55 then you may be able to force them to sell. It depends on what the by-laws say about violations of the by-laws.