That's frustrating! Sorry you guys have to deal with all that instead of just being able to be excited that you have given your little girl a name that you love!
I'm surprised that your MIL doesn't give a 2nd thought to the idea that you guys may be using the mn because it's also your name (or maybe she doesn't know you guys share a mn?...) It's awfully presumptuous to think that the fact that it's your name had no bearing on the decision to use it, kwim? And, I don't know about you Mom...again, it
is somewhat silly for her to just go about assuming that you guys chose this name because it's close to hers...heck, many names may be close to hers! She's kinda stretching here because she WANTS her gd to be named for her!
What would I do in your shoes? That's a hard one. You have 3 choices (4 if you include changing the name...) If I really loved the name and really, really didn't want to change it then I would either 1) grin and bear it (figuring that you guys know the truth about her name- and can later on even tell your DD the reason behind her name before THEY do!) or 2) I might just slip into conversation (or apparently 2 conversations...) how the name came about. You can do it in a laugh it off as you explain it way when they are one of their tangents about the name ("Oh, yeah! *chuckle* I nearly forgot that xYz was YOUR mn as well as MINE...that didn't even come up during the naming process!" or whatever...) or 3) you can be upfront about it and try to be as sensitive as possible..."I'm really sorry for the confusion about DD's name and how it came about...but it's really upsetting to me to hear you using my DD and her name as a way to hurt other's feelings because you think that we chose the name on your behalf. Here's the reason that we named her what we did...."
You may want to think about letting them know what's up at some point soon if you decide to keep the name otherwise you are going to have a long road a head of you listening to them...I doubt that the bragging will stop. DH's family still brings up that we named him (mn) for his g.pa...I don't mind them always reminding people of it (because we DID give him his name) but I'm just saying that after 2 yrs it still hasn't gotten old to them!
GL...and as a side note- I 2nd the idea of next time keeping the name to yourself til birth. That has been a wonderous thing for us this time around and I wish we would have done it the other 2 times!