I can't stand being reminded that my girlfriend has kids.
She's always going to have kids so why does it bother you to be reminded of this?
I know she might be spending time with them while I'm not around
You should accept that your girlfriend has kids and they are important to her. If you can't, maybe you should avoid dating people with children so you aren't resentful of your partner.
You do that, being reminded of your girlfriend's kids. I bet you are enjoying it.
I wouldn't mind it if I choose to date someone with kids. You made the choice to date her to either accept it or find someone else. It's unfair to make someone feel bad for having kids and her kids were there first before you.