Most Helpful Guy
I think you a making way to big of a deal about this. I understand you're hurt, but this probably has a lot more to do with resentment of your ex and the new girlfriend rather than how she is with your child.
Sure, the discipline in front of you could be considered wrong, some might even disagree with that. But heher making a mothers day craft with your daughter for you is a peace offering.
I don't want to sound rude, because I understand your frustration, but I think it's wrong to not accept that gift from your daughter, regardless of who she made it with.
Your daughter will always remember how you didn't accept her gift, it will also teach her that it's okay to act emotional on these big issues, rather than being calm and collected.
The bigger thing to do is to accept the gifts, act cordially towards the girlfriend, and never bad mouth your ex or the girlfriend in front of your child.
You should let your child make up their own mind on who the bag guy is. It's got to be infuriating to watch another woman with your ex raising your daughter while you do it alone, I get that, but this should always be about your daughter and not the girlfriend.
Most Helpful Girl
You're going to have to get over it. This woman could turn into her stepmother and they're inevitably going to have some sort of relationship. She's like a parent figure to your child too, even if she's not her biological mom.