What is the proper way to combine past tense of do (did) with multiple bare infinitives in a question:
- Did you go to vacation or stay at home?
- Did you go to vacation or stayed at home?
- Did you go to vacation or did you stay at home?
The last one is always correct, but I assume shorter form is more desirable, especially if more than two verbs are involved: Did you go to vacation, stay/stayed at home, go/went to work, or do/did something forth?
Also, if the second form is not correct, could it be transformed to Did you go to vacation or you stayed at home? I assume that this form has a little bit different meaning, because the emphasis is on vacation, and staying at home is just mentioned as one of the alternatives. Basically, this form can be answered with Yes or No, while the aforementioned three ones cannot (I offered two equally probable alternatives in the question). Does my reasoning on this make sense?
I am not a native English speaker and I caught myself using the second form occasionally (although it seems to clearly break the rule auxiliary verb + bare infinitive).