In adoption there is loss by so many more people than just the firstparents. Extended family doesn't have a say necessarily in the placement of a child either, and they too must grieve that which they have lost. My guess would be that they're not trying to hurt you or undermine your authority by calling your daughter L, but that they're having a hard time adjusting. It truly may not be your DD's firstmoms fault they are doing this, so I would encourage you to try to separate that issue so as not to blame her for it.
As for the other issues, I agree with the others that you need to communicate your concerns earlier rather than later, in a polite and tactful way if possible. When I was first in my OA with my daughter and her Mom there were so many unknowns. We're a year and a half in and I'm still always worried about saying the wrong thing or doing the wrong thing. Having her Mom be upfront and honest about her concerns would be welcomed.
Also, because she signed something "Mom" doesn't mean she's going to challenge your role. Maybe she will, and maybe she won't. Again, this is definitely your right to discuss. Personally, it takes a while to adjust to the fact that for nine months you were "Mom" to this perfect little person growing inside you, and then in one day and one signing of a document you're not. Signing the card "Mom" may have just been a way of showing her continual love for your daughter.
I'm beginning to ramble and be repetetive! Sorry!!!
Again though, I can't say enough - talk to her about it. Best of luck!
