L., have you ever watched the TV show "Extreme Couponers"? Your friends reminds me of that, except she doesn't clip coupons. She looks for the cheapest things she can find and makes things to give away.
My parents had college friends who were like this. They were so cheap that they didn't put a nickle in the pony in front of the dime store when they put their little girl on it. She didn't know it moved, and got mad at my daddy because he stuck a nickle in it for her.
They ate the cheapest food they could find for at least 40 years. Now at their age, they have learned better about healthy food since they have so many physical ailments.
They always gave us really cheap gifts as children, including baby gifts when we were 7, 8 years old.
Look, they were besties with my parents. My parents loved them and looked past it. I remember my mom chuckling when we opened the gifts. I'm so glad she chose to feel this way rather than the way you feel.
All of us have idiosyncrasies, L.. I promise that you do, too. How would you feel if your friends dumped you because of something that bothered them about you? The question is, do you like the part of her that doesn't have anything to do with her cheapness? If you cannot stand your kids playing together because they are brats and hurt your children, to be honest, THAT would be more of a reason to walk away from her friendship than the fact that she is cheap. If she asks why you aren't getting together with her and the kids anymore or why you aren't willing to babysit, you should just say "I'm sorry, but our kids can't seem to get along and I can't have my kids getting sat on and hurt. Perhaps when they are older, they will get along better."
One of the things I urge you to think about is that you really do NOT know what her finances are like. It could be that she simply cannot afford to do more than she does. Yes, it would be better to give a $5 gift card to the grocery than a gift with 2 missing items in the box, but she doesn't seem to understand that she looks bad to other people. This is certainly a social gaffe, but she either cannot recognize it or doesn't want to. You call it calculating, but I'm not sure why you feel that you can characterize her cheapness as calculating. What you are saying is that she is intentionally trying to stick her finger in your eye with this.
Regardless, you must make a choice of what is most important to you - a friend whom you like regardless of her ridiculous gifts and eating your food without sharing in kind, or walking away from the friendship because this issue means more to you than she does.
Whatever your choice, I do think that you would do well to try not to judge others as harshly as you do. You don't like being judged harshly yourself, I'm sure.
Dawn