The grammatically correct way to say it is 'my husband and I' or 'my daughter and I' but in a general conversatiom we would say 'me and my husband' or 'me and my daughter' anyway. You can say 'my ... and I' in a conversation too, it doesn't sound wierd either way, only in writing you have to write 'my ... and I'.

I think it would be grammatically wrong despite the use of a main clause starting with "we went". The use of "we went", I suppose, acts as an addition for better understanding (although in this context it is pretty clear who did what), but if you were to remove the pronoun "we", you would have "Me and ... went...", which is obviously wrong. We don't say "me went" (because it is an object pronoun, you also wouldn't say him/ her went), rather you could re-phrase it as "My husband/ daughter and I went ..." and that way you would not have to add in the pronoun "we", which might give the sentence a more fluent tone ^_^

In this statement you would use: "My husband and I went...." "My daughter and I went..." -- You do not need to use we in that since you already are specifying you and your husband or you and your daughter. -- Went is a past tense of go. At some point in the past you guys have gone "somewhere".