[Oceans]

If this is bothering you then yes, have a talk with her but I have a few thoughts as 1) a bmom and 2) a bfamily member.

I would bet that the card was difficult for her to sign. I know if my family member (who is almost 5 months into a very happy and healthy OA) had to sign a card to her DS, it would give her pause. I don't believe she thinks she will be referred to as her first name but I don't think she expects to be "Mom" either. After reading your post, I'm going to suggest she bring that up with the parents sooner than later so that this situation doesn't happen to her. Maybe instead of correcting her (that she is not Mom) you could spend time on your next visit deciding together what your DD will call her someday and then start using that name consistently when she is around. For example... E, look who's here it's (insert name here)... Just a thought for a positive way to correct her...

As far as the family referring to the baby as L... The bmom probably doesn't have much control over that and if she is correcting them, that's all you can ask her to do. Again, this happened in our family quite by accident early on because we knew the baby as X prior to birth and now he is Y. This isn't her fault and I would probably let it go to be honest.

As far as the bdad situation I'm not sure what to say other than I personally take third party conversations with a grain of salt. Who knows what context she said this in or the actual intent when she said it to the bdad. She could have been encouraging him to forge a relationship with you and didn't mean "just show up" but rather reach out and see if it was OK to come... It's a possibility anyway. She shouldn't be inviting him to your events by any stretch but again, third party conversations are always sketchy... I might ask for more details from the bmom before I assumed anything.

Also, I think it will be hard going forward to dictate what she can and can not say to the bdad if she has contact. I'm not even sure if its even "right" to try. I understand you want to maintain some privacy but it's probably unrealistic to assume that she wont be giving him updates if they are still in touch.

So yes, I would have a conversation about this if it bothers you but I would encourage you to look at this as an opportunity to more clearly define each of your roles instead of seeing it as a challenge to your position as DD parent... Because ultimately, she can't challenge that and probably wasn't doing it on purpose.

I hope this makes sense. It sounds like you have a great foundation and I wish you all the best of luck...