Invitations… who to invite vs announcing the wedding

It's best to send any wedding announcements, holiday card marriage announcements, or social media posts until after the wedding. As a good host, you want all your invited guests to feel welcome to your event. Sending a disingenuous invite or an engagement announcement that could be misconstrued as a Save the Date will result in hard feelings, something you don't want.

Definitely don't invite anyone with the wish that they won't come. That's also asking for trouble.

Honestly, if the situation is tense with these people, I wouldn't do anything at all. If they are rude enough to ask about/for an invite, I would say "we're keeping it small, so can't invite everyone we would have wanted, but love to catch up with you after the wedding!" or something like that.