Problems with newly discovered half sister

Last year I discovered I have a half-sister via a DNA company. My dad never knew she existed until now and it’s been a shock to all of us. She said she had spend her whole life wondering who her birth parents were. Despite the initial shock we were happy to connect with her and looking forward to getting to know her better and form a bond. She has also recently managed to find her birth mother but after just one meeting with her she doesn’t seem intrested in getting to know her further. Apparently her birth mother has some mental health issues. (Not surprising concidering she was forced to give up her baby at birth). The trouble now is that my half sister seems really keen to get to know our extended family of aunts, uncles and cousins as well and has reached out to some of them already. We don’t have a good relationship with them following many issues over the years. They’re very clearly wealthy as they own businesses that would make it obvious and I can’t help but wonder why my half sister is so drawn to connect with them, despite the challenge it poses us, (given we don’t get on), all while discarding her vulnerable birth mother so quickly. I’m starting to feel like she might be an opportunist. We outlined our difficult position to her but she snapped that she had a right to get to know who she wants. I just think it would be best given the complicated situation that less people should be involved , or at the very least only primary blood family. We then took a step back from connecting with her as often and she lost it saying how she feels rejection acutely as an adoptee! This rejected adoptee narrative is often played out in the media and I find it tiresome to be honest. My dad never knew about her and her birth mother had no choice but to give her up. If anyone is doing rejecting it is she who is rejecting her birth mom and not showing interest in the challenge she is placing us in. I have to be honest that I feel a little rejected here, like me and my Dad arent enough. Any thoughts on this? Should we be weary? My friends think wev been done a favour!