@@IdiotsIdiotsEverywhere you've changed the context in last updates of your smug comment about her ( aftersmuggery 
), very different to your OP & first update.
But you still indicate you're angling to turn up at some of the same events. If she wanted to tell you, she would! 
I think that @RibbonAurora and @Laiste both made excellent summaries of what you can't see in all of this, of how you are coming across. As do other PPs.
Whether you intend to or not, you're THE family member likely indicating they may engineer a bump into her family with yours, and may use it as an opening to tag along "for the boys' (same aged DS's) or to suggest meeting up later. Maybe she just doesn't want that and can't say without offending you.
And FWIW if you keep saying 'oh you're not doing anything too, so pop round if you're free' and they haven't taken you up on it, they just don't want to! So by the third time you've said that, she might have become fed up of feeling beholden or rude for not 'popping round', hence using a more vague ' sorry we've plans' instead... To not be rude!! (Why not leave an open invitation for her to text you if they ever find themselves at loose end to see if you're all at one too ?).
You asked at start AIBU?. Majority PPs have said "Yes OP YABU". Even after your latest updates changed context, MNers are saying Y(Probably)ABU with the sense of underlying expectations that comes across.
Maybe it's how you are phrasing it and you're not pushy in RL, but it is worth reflecting on responses of MNers. And instead find other family/ies of similar aged DS who do want to share event news with you and to sometimes hang out with your families together at the weekend. And go to cool events you've found!
If your relative really is saying 'we've got plans' as part of a cunning plan to 'aftersmug' you as you've interpreted it, maybe be less forthcoming about your plans and she'll be asking you more ahead of time, once hearing about the fab time you had with your buddies!! Then you can 'sorry we've got plans' her back
if you like. Or your relationship will be more even.