My FMIL got her dress. It is a very pretty purple dress. My mother found a dress she really loves and it also happens to be purple. My mom will not wear that dress though because my FMIL is wearing purple and she feels they would look like sisters if they wore the same color. They look nothing alike and the dresses look nothing alike. My wedding is black tie and my mom wants to wear a skirt and button down combination that does not fit the formality. Do you think I should bring up that I would prefer she wear something else since it is not as formal as it should be.

Mother of the groom's dress

Purple dress my mother likes, but won't wear

Outfit similar to what my mom already owns and wants to wear, but I don't think is considered black tie formal
Re: Mother of the Bride
That said, if you can't convince her, don't essentially say "I really wish you would dress up more." Tell her to wear what she's comfortable in.
I agree that outfit will look very out of place at a black tie event.
But if your mom decides to wear the separates then let it be. She presumably knows your wedding is formal, and this is what she is choosing to wear.
My mom knows my wedding is formal and she knows how fancy my venue is since both moms went with us when we were looking at venues. I feel like she is now just being spiteful because I think she expects me to tell my MIL to wear a different dress in a different color which isn't going to happen.
ETA - JK I was thinking the top dress was your mom's but that's your MIL's.
Personally, I'd rather match the MOG than spend this kind of money on a dress, but maybe your mom would like this one?
https://www.davidsbridal.com/Product_gathered-jersey-dress-with-scalloped-lace-bodice-a18436_all-dresses
https://www.macys.com/shop/product/betsy-adam-plus-size-sequined-lace-ruched-gown?ID=6593563&CategoryID=5449&RVI=Search_2&tdp=cm_choiceId~z6593563~xcm_pos~zPos2
I agree the outfit she is now planning to wear is not formal enough for a black tie event, but it's a victimless crime. She knows your all's wedding is black tie, so that's on her if she ends up feeling underdressed.
Whether she is purposely being spiteful or not, don't rise to the bait. I'd let it go and just keep rinsing and repeating statements like "wear whatever makes you comfortable".
Seriously it sounds like mom is being a pain in the ass just for the sake of being a pain in the ass. She won't wear 1,000 different appropriate dressed but she is willing to wear the one inappropriate thing she's got? Fine. G'head.
She could wear this. I’m sure she’d be the only one!
Let the entire thing go.