You can't make people like you under the best of circumstances, and you certainly can't make them like you while you're actively badgering them on what you perceive to be their failures of conscience.

The only answer that has any chance against against the information saturation kids face these days is to talk openly with kids, early enough and often enough and unflinchingly enough that you set the precedent of being the safe place they can go to ask their difficult questions. It has to happen starting when they're 2 or 3, and they ask you where babies come from and instead of freaking out and deflecting, you give facts commensurate with their ability to understand.

Moving is hard. Staying is easy. Logistically speaking, at least. And this is true whether you're doing or undoing something.

Apparently you have ample proof from experience that you're not going to stop world evil by debating your in-laws into submission, so it's okay to choose not to try.

Plan your own vacations when you want to, and plan a suitable combined vacation with this other family when you want to. If they freak out at your planning your own vacations as you see fit, then let them. Bowing to unreasonable demands because someone will make you pay emotionally if you don't is not a healthy option.

If you take the time to listen to an upset child's story with empathy, and guide the child toward figuring out the root of the problem, then the result is often that the child not only calms down, but also in the future is less likely to get so upset.

Unfortunately, I think the expectation is that birthday girls don't pay.