I'm in my first poly-relationship and it’s a LDR. His GF (since 8 years, she's the primary) can't deal with the situation. She's also poly and has a BF besides him. We have a LDR so we only see each other once a month (for 2 days). But every time we have a date, she's texting him that she feels like shit because he's out with me and even when we she has a date with her other boyfriend she uses her right to veto to forbid him to see me when I'm in town. Last time he wanted to see me, she broke up with him (but one day later she apologized). We still had a date that day. Is that normal when a new person joins to behave that way, or is it me who is overthinking it? I don't know what to do in the current Situation and I don't now how to think about her behaviour (i feel very hurt by it). Last time she texted me and said that she's the primary and she should be the most important to him and if she doesn’t want us to date she expects him to drop me.
No, her behavior is not appropriate at all. This is not healthy polyamory. That’s not really how “right to veto” is supposed to work, and texting your metamour to say possessive things like that is, at the very least, extremely rude. Your feelings that she is out of line and being hurtful are entirely legitimate.
Have you talked to your new partner about this? Your relationship is, in the end, with him and not her. Have you told him that her behavior is hurtful to you? Is he willing to stand up to her and set his own boundaries, like saying that he won’t be fielding texts from here while on a date with you, or that he won’t honor a last-minute “veto” demanding he cancel a planned visit with you when you’re in town? Does he agree with her that your relationship with him will always be on a less secure footing than theirs? If he’s willing to work on this and gives you clear evidence that he can actually make progress, then you can decide whether you want to wait that out.
If this seems like a pattern he’s pretty committed to, and he’s not willing and able to make any changes, then you’ll need to decide whether you want to stay in a relationship with this much drama and uncertainty attached. Do you want to date someone who thinks it’s okay for their other partners to treat you like this? Do you want to be part of a polyamorous arrangement with a person who behaves like that? If you decide to stay, at least be clear-eyed about deciding that whatever he offers is worth putting up with all their nonsense - don’t be thinking that you can somehow convince her to be reasonable.