notification came to wrong facebook page

Do you mean Facebook page, e. g. the kind of page that might be a fan page for a celebrity (Fans of Mick Jagger or whatever), or are you talking about a Facebook account, which is your account and your significant other's account (Dave Smith and Mary Smith, for example)?

I am guessing you mean the latter, and so I am reading your question as you having joined a group (People from Newark, New Jersey or whatever) with the Mary Smith account but now want to join the group with the Dave Smith account. I am further assuming that the group is secret or private and therefore it requires an invitation before you can join.

So ask the group leader to send the invitation to the correct account and join. Then, if the other account is in the group, have the other account leave the group.