Syntactically, it is the copula
だ with conjunct
が, probably used in a cleft sentence with some omission.
が often connects contrasting clauses, but as with this case, it can just connect two clauses that do not contrast. The literal translation is
'On top of the fact that (it) is my uncle who lives close-by (that I am going to talk about), I've heard that he isn't doing fine lately.
A more natural translation may be close to yours:
'Speaking of my uncle who lives close-by, I've heard that he isn't doing fine lately.
The mistake you made is the scope of
最近 'lately'. It should not be "heard lately" but should be "not doing fine lately". Or, maybe you took that correctly, but your translation is ambiguous.