No , it wouldn't be so bad. Issue the invitation (well it has been issued) and if she chooses not to come, that's her choice . Certainly don't put her under duress and have her behave badly while saying ' I'm only here because you insisted ' etc. just make it clear: it's your wedding, you'd be glad to have her there to celebrate and have a good time, if she feels she can't do that, you are FINE with that, you'll see her sometime later.
Stand together, stay calm, don't let her do divide and rule, or get competitive 'my son's family / my DILs family etc).
DH just sticks to his PoV . 'You are invited Mum, we've kept it to a very small event and invited those we see often and are close to. That's the way it is, it's not a competition between families, come if you would like to, but if you fe you can't fit some reason , I don't need an explanation, just decline'.
Invite your sister if that is what you and DH want to do.