My Mother has become very rude to people when we go out. She will walk into a restaurant, and tell the Host very loudly, "I better get a good meal, because the last time I was here the service and food were lousy." Then she repeats this to the waitperson, complains about the menu items, there is too much food, etc. My Father feels that this is a normal part of old age, and that I should tolerate it. I told my Father that I do not want to go places with them since my Mother cannot behave appropriately. My husband and children are embarrassed when these incidents occur. I do not feel that I am wrong in not wanting to be put in these situations. My Father says that My Mother will not go to the Dr. to be evaluated for Dementia/Alzhheimers/depression. I bought the book, "Coping with your difficult older parent" which is extremely helpful, but our relationship is so strained.
She may have depression or dementia or just be old and cranky.
If this is a pretty big change in Mother's behavior, I'd suspect a change in her health. People who have been polite adults seldom become disagreeable overnight just because they got older. Anger can be a part of depression. Lack of social inhibitions often goes with dementia. Anxiety can come out as aggression.
If Mom is behaving this way because of illness, this could be an opportunity to demonstrate loving tolerance to your children, especially if your husband can get on board with it. I know people who have cards printed up to hand store clerks, waitresses, etc. that say something like "Thank you for your patience. Mom has dementia." Most people are remarkably kind when they understand the situation.
If your mom is "in her right mind" she might be persuaded to restrain herself somewhat if she really enjoys your company. But if she is cognitively impaired in some way, she may not be able to make the logical connection between her behavior and your absence (even when it is explained many times.) You may not be able to "teach" her better behavior, but you can protect yourself from being embarrassed by it by either accepting that that is how she is and it is no reflection on you, or by simply staying away.
Spend time with Mom in her house to figure out if she's losing it. Can she still get a cup of tea? What did she have for breakfast? Can she find bandaids and ointment for a cut? Ask questions about things that happened last week that were different enough to remember. Send the doctor a letter listing the behavior you are worried about. The restaurant behavior is not proof of dementia without more evidence.
You can stop those remarks at the time, or de-fang them, by saying, "Mom, isn't this the restaurant where you don't like the food or service?" while winking at the manager or waitress. It's 50-50 she will scold YOU for being impolite! Or say, "No, Mom, that was at McDonald's!" Or say, "Mom, don't let them know you're the Phantom Gourmet!"
This is really embarrassing, but she isn't capable of changing it. If you can't or don't want to maneuver around it, if it makes you unhappy, then you have our permission to stop going with her.
My mother on the other hand, before dementia came into the picture, was one to be reckoned with. She has a personality disorder to begin with, but she would never confront a situation with people outside the family unless you were with her. That was embarrassing to me many times. Mom usually had dad fight her battles for her whether she was right or wrong..What mom would do if she had a complaint with a next door neighbor, when I was visiting and the neighbor was outside, she would start making rude comments about them very loudly to me. I would ignore her and make an excuse to leave as quickly as I could. I know the neighbor heard her. One neighbor took my mother in stride and could deal with her. Mom would leave notes on his truck because he would park it under a little tree planted near the sidewalk. He parked there for the shade in the summer. Mom's notes would say, "Do not park your truck here, this is my tree and my shade for my car!" He respectfully did not park there so they got along. The neighbor on the other side of mom was not as accommodating. He resented my mother and would go out of his way to anger her. My sis and I tease the neighbor who accommodated her, whenever he parks his truck under her tree (mom is no longer living in her house), we jokingly tell him, we inherited the tree, LOL!!
If you must go out, maybe you can limit to food court when with mom. I know it's not fun, but I would adjust my dining out experiences to those that are least stressful and you can all have a pleasant experience.