If you're an abuser, you are also superhumanly good at consistently lying about how you care for your children. Seriously. If Emer needs the vaccination (which she does), and she doesn't want the vaccination, then you can either let her go unprotected with the risk of getting seriously ill in the future or you can use a certain amount of force. That's a crappy choice to have to make but it does not equal abuse. It doesn't. Her phrasing was unfortunate, but I really do think she was expressing an understanding that you keep her safe even when nasty things sometimes have to happen.

Part of maintaining the trust in a parent-child relationship is about both of you knowing that the parent is competent to run the show. It's totally appropriate to say you're sorry when you have to do something she doesn't like. But I think it's possible to overdo the contrition, and that would make her feel much less secure. You are very aware of how things might affect your children and that is fantastic, but you and they also need to have faith in your judgement. She will be OK, and your knowing that will be reassuring to her.