My husband, son, and one daughter thought Mother's Day was last week, thanks to the early advertising this year. I've told my son I am not his mother, and the kids that a simple phone call is plenty. The daughter has already fulfilled her duty in remembering me, albeit a week early. Better than late!
As to these letters, I'll bet almost everyone's answers are strongly related to their age and whether they are mothers and whether their mothers are alive. I look forward to the male perspective.
1) I couldn't say whether this monster is of your own creation. However, it is fair to ask that she either spend time with you, or find accommodations elsewhere, particularly if you are also hosting her guest. E-mail her back, and be more clear. Tell her that is she is coming to see you, she is welcome, even with a friend in tow. Also remind her the the kids are always welcome. However, be firm that if she is using your home merely as a place to leave her clothes while she's out, that you cannot accommodate her. (Gotta wonder about this "friend.")
2) Try asking her out without your mother and grandmother. She probably feels she is playing second fiddle to your family, and rightly so. While the 3 of you discuss old friends and family, she likely is feeling left out in these group gatherings. If she still refuses, take a "picnic" over to her house, to enjoy out back, if she has a yard. (Sounds like Prudie has mil issues.)
3) Try talking to your husband or try finding a cheaper groomer. Self-serve is a good idea, except it would fall upon you or your husband, since the kids are probably too young to do an adequate job. Personally, one of my requirements for a dog was short hair, especially living in the south.
4) Deal with it. I know parents can be embarassing; it's part of the job description. However, by getting to know your friends, your mother is trying to make sure you are with a good crowd and making good decisions. Try thanking your mom for driving you. Maybe she'll let up if you show some appreciation.