7 Answers

The reason the first sentence is correct is because you have a plural subject (dad/siblings) .
 THEY WANT.      THEY WANTS.   (Obvious)
 IF the sentence read, "Neither (want, wants) to go....."  wants would be correct.. 

First sentence

Option A is correct

Sentence (A)

(A) is the correct choice because of the plural subjects. If you listen to the sentence being spoken, it also sounds better.

NEITHER sentence is correct! 'My dad... want to go...' is obviously wrong, so you can't have 'want'. The alternative 'my siblings wants...' is also wrong, so you can't have 'wants'. You've got to have something like 'My dad doesn't want to go..., and neither do my siblings'.

correct subject-verb agreement 

neither my dad nor my siblings want to go to the reunion this summer