difference between might and would in the past

might does not really denote habitual action in the past, although in this phrase the meaning of habit touches it because of the second 'would' ('she would always please him').

I would rather connect might with However as they occur in structures like:

However this might affect her family, she will still have to leave.

Might is rather related to the idea of possibility or eventuality, and that in the past, as well. So your first version of the sentence looks like a habitual possibility in the past, if that makes sense, and it is habitual because of the context, not necessarily because of might. I understand something like:

However drunk it would be possible for him to come home, she would always please him.

As for would in your second version of the sentence, I do not think there is any ambiguity there.