Do you mean "Guardian ad litem?" If so, they will meet with SS as part of the whole process as they will be representing his interests. How does he feel about the custody change? At 14, his feelings will be taken into consideration, not matter how bad BM may be.

I would be treading very carefully here. 

Is this a change that SS wants?  Has his father talked to him about it?  Is BM's alcoholism both officially documented and untreated at this point?  Are her actions or condition actively presenting a danger to SS?

I would guess unless you can absolutely say YES to all three of those things.. that the courts may be reluctant to change custody at this point in his life.  

Stories abound on here with father's who sought more custody and went back to court only to come out of it paying hefty legal bills and with sometimes HIGHER support obligations.  So, unless this is a real change that his son wants?  Unless his son is suffering from abuses or neglect? It's going to be an expensive exercise in futility.

And... I don't mean that he and his mom had a fight and in a fit he didn't want to be there.. it's likely at 14 he has roots where he is.. school (not sure if it would be the same).. maybe sports teams.. friends.. and at that age, he is capable of doing a lot for himself.. feeding himself.. doing his laundry. etc.. he isn't just a helpless 5 yo.. and he may present that he is not suffering there.

And.. if BM is seeking help for issues, the courts may not want to punish her for that.. and won't change custody.

Again.. your husband may have endlessly deep pockets. but there are way too many lawyers who are happy to run up the bills for shot in the dark hopes and dreams.  So, unless there is a real and legit reason for change (and mom having wine daily in itself isn't enough).. unless the CHILD wants it.. it's going to be uphill imho.