am I a bad friend for not wanting to invite my guy friend's girlfriend to my wedding?

I have a guy friend who's mostly been single, and he's now in his first relationship. we've been best friends and used to talk about everything.

he met her in october, I met the girl 2 times in February, and i kinda got weird vibes from her, i felt like she wanted to dominate every conversation and even was a bit weird with my fiance (giving him a bit extra attention?), and i felt sidelined in the group setting (4 couples) with her in those two times.

i wasn't really sure if it was just me (because i take time in trusting new people, i'm guarded)

my guy friend talked to me about her a lot and about issues they had, she sounded a bit unhinged from what he told me (locking him out of their place when they had a fight, blocking him, etc.. pushing him to get married) and i was a bit worried for him because it didn't sound healthy.

sure enough in march they broke up. and we all consoled him and he told us how unhealthy the relationship was. they were living together at the time and he was looking for a new place. they ended up getting back together after a week but he didn't want to re-introduce her to the group yet.

in may they broke up again, again looked for an apartment, etc... and 2 weeks later got back together, back to living together.

my wedding is this june, and i told him it's quite intimate and i don't feel comfortable having her there - cuz i only met her 2 times. (but besides that, i didn't really feel like dancing with her and paying much attention to her since i haven't seen her since feb, and i'm a bit guarded about at her because of all that she's done to him, i'm a bit scared she'll cause a scene there for some reason)

at first he said he understands but after telling her she wasn't invited - he tried to push me to invite her anyway, wdyt?