Am I missing something? You're annoyed because she wanted to run faster than you did, and you stopped off because she wouldn't slow down to adjust to the pace you wanted to run at? If I've read that right, you are being incredibly unreasonable and borderline ridiculous.
Do you always run parkrun together? I'm failing to understand what was wrong with her going off at her own pace? I've done hundreds of parkruns, many with friends but many more solo. There are no laws that someone has to adjust their own pace up suit you when you're both adults who can simply wish each other a good run and meet again at the end.
I take each parkrun as it comes. Sometimes I feel like going for it but often I'm happy to just go with the flow. My plans often change partway through, depending on how I'm feeling. Sometimes I've run off ahead of a friend I started with, with their blessing. Other times I'm the one telling someone to run ahead and enjoy their run as I'm just not feeling it today and don't want to spoil their run. Even if you originally plan to run with someone else, plans can and do change depending on how each person is feeling throughout the run.
You have taken this way too personally. No true runner would ever stand in the way of another fellow runner pushing for a PB if they're feeling on it (especially if that other person is a close friend, partner or family member). Why should she have sacrificed her own run for you, just because you wanted to take it easier? If you're that joined at the hip that you're annoyed at her for running off ahead of you, you might need to evaluate a few things because that's quite suffocating and controlling behaviour.
You said it yourself, it's only parkrun. I absolutely love parkrun, but finish times are hugely irrelevant. That's not what it's about. You both got out in the fresh air for some exercise. That's all that matters. You really don't need to run together to enjoy it or get something out of it.