Florida, where I live, is a weird common law state, I do believe. ...
"Common-law state" (there are 49 of them; all except Louisiana), and states which recognizes common-law marriages, are two different concepts. As noted, Florida doesn't recognize common-law marriages, perhaps other than those established in those states which do.
OP writes that "the State of FL ordered child support". Was there a court order to this effect?
I'm assuming "the Executor his son" is executor of the ex-wife of the decedent, and not of the decedent himself.
One would also have to determine if this woman who lived with the decedent for 30 years was on the title to the property. If so, she might have a claim to half the value of it.
In the title of this thread, OP writes "estate given to partner with lifetime rights?". If the decedent gave her a life estate
before he died, and the child support claimant failed to record the foreign child-support judgment, she (the woman who lived with the decedent for 30 years) might have a case.