Should my future brother in law’s gf be invited to wedding

ki

My fiancé’s little brother just started dating some girl he met online. Whenever I go visit to his moms house they always walk in and go straight to his room. I’ve never spoken to her nor do I even really know what she looks like. Me and his brothers and their wives always mingle in the living room and she never sits to try and get to know us. I’m having a very small wedding and I don’t want people who I don’t speak to, to be there. I get that’s his bro’s gf but they’ve been together for 2 months and she’s never spoken to any of us. Last week my fiancé asked if they wanted to join us for board games when they walked in the house and she walked straight to his room, and he said no. I’m sure he’s gonna be upset at the fact that his other brothers wives are going and are he’s gonna be the only one without a date but I actually have relationships with them (that I created).