Often when I see this, it's referring to one member of an established couple dictating what the other relationship (that they are not part of) is going to look like or function as. This is inappropriate.
My question is, does the same standard apply when one member of an established couple falls in love, decides to be polyamorous with new partner, thereby mandating a conversion from monogamous relationship to a polyamorous framework (or no relationship at all)?
While I don't think people should just start another relationship without checking their existing partners are okay with it (in my opinion, doing something you know your partner isn't okay with is cheating, even if you don't hide it from them), I think there is a big difference in that the former is someone saying "you shall (not) do this in your other relationship" and the latter is someone saying "I shall (not) do this in my other relationship".
In the latter scenario, the person trying to control the other is the monogamous person. At no point is the poly person from your example trying to pressure their partner into starting a relationship they do not want, or forbidding them to start one they want.
That our partners' lives affect us is a fact. And in any decision that might affect a partner, they should be consulted. It's true of changing jobs, moving or getting into another relationship. But in the end the decision should always be made by the person who has the opportunity for a new job, a new location or a new relationship. They should take their partners' feelings and opinions into account, certainly, but the decision remains theirs.
Similarly, someone's decision not to have children will affect a monogamous partner who wants children, as their monogamy doesn't allow them to have their children with another partner. However, it remains the childfree person's decision whether they want children or not, and they are not "holds more power over a partner's other relationships than is held by the people within those relationships", where the relationship here would be that of parent to (currently nonexistent) child.
Because the person who wants children can still make their own decision as well. Do they want children more than they want the relationship with their childfree partner? Or do they want the relationship more than they want children?
Similarly, the childfree partner presumably made their decision with the understanding that they might lose someone they love, and that they can't force their partner to stay, however it's important to them that someone else doesn't make the "having children" decision for them.
To put it in a polyamory context, or in a mono-poly context, I do not want biological children, but I am absolutely fine with any of my partners having them. I don't control their desire to have children, nor do I wish to. If they have children it will affect me, and I am aware of it and fine with it (otherwise, I would have the possibility to decide to leave a relationship that wouldn't work for me - this is always an option) but I will retain my own autonomous control over my own body.
Similarly, if I wanted to stop having sex with my partners, I wouldn't forbid them from having sex with others. I would retain control over my own body and make my own decision not to have sex, but that wouldn't be a decision over their body and their ability to have sex, as they would still have that option with others.
That was the case with my ex, during the times I lost trust in him and there wasn't much intimacy, but we were already open so although he never ended up having sex with others because he wasn't interested, I refuse to take responsibility of his lack of sex because I did not forbid it or try to stop it, and it's a decision he made himself not to pursue it with others.
I hope I'm being clear here about where the line is. It can be tricky, because of course what other people do will affect you, and you want basic respect and courtesy in being informed of it and being given a chance to give your opinion, but there is a difference between things that affect you but are someone else's personal decision to make, and things that you should retain control over because they are your personal decisions to make.