I've only read the OP, but its your wedding and you get to decide who you do and dont want there.
1. Get on with the wedding, dont worry or pay her any attention.
2. If you wnat to be conciliatory, then you cna send her a short e-mail saying soemthing like sorry you were upset, but we decided as we have limited cash etc that we prefer a small wedding. To be fair on this we have only invited direct relatives and none of the extended family(assuming this is true). I know you will understand and respect out wishes etc.
Tbh I'd do 1 and wouldnt care as you have already explained once. A firend and someone you would wnat to be there is someone who wishes you the best and respects your wishes. This cousin does neither +++++++++> clear conscience..