When I was a child many years ago my family chose a maximum dollar amount to be spent so that everyone would get a comparable present and no one would go in debt.
I think that most of the people giving your children gifts want to see the gleam in their eye as they open the presents. An inexpensive toy will do this just as much as an expensive one. My grandchildren, aged 7 and 4, love their "Dollar Store" gifts as much as others. Last year, for my granddaughter's birthday I took her shopping at the Dollar Store. I did spend nearly $20 and it was so much fun for both of us. One thing that she chose that surprised me was stemmed glass with fruit painted on it. She drinks her milk out of it at my house. She chose artificial flowers which decorate her room and her mother's entrance hall. She chose several helium filled balloons and bounced them around for a week or so. She also chose a couple of stuffed animals and a small metal planter in which they rode as she pretended it was a gondola attached to her balloons. We both had wonderful fun. She was more interested in a larger quanity of choices made by her than in just one thing from the toy store. She has a difficult time deciding on just one toy at the toy store. And all of the items were inexpensive and have for the most part disappeared or put to other uses.
Children need presents at Christmas time. I agree that they don't have to be expensive nor should they be something that your children will only play with for a short time. I notice that one of your children is 12. She probably compares her gifts to those received by other girls her age. It's important for pre-teens and teens to have some things that are popular at the moment. A wish list is a great way to find out which ones are important to her. Our family exchanges wish lists.
Little kids can write a letter to Santa including their wishes and you could copy it and send it to your relatives. Whether or not you also add that donations to their college fund is also a wish depends on the personality of the person receiving the comment. My family sees each other several times a year and this sort of thing is discussed at times not related to Christmas. That feels less intimidating to me. It's a part of a discussion similar to the one you started on Mamasource. And by making your wishes known as a discussion it allows your family and friends to decide for themselves.
I liked the idea of suggesting that people could contribute to activities such as art, music lessons, karate, etc. The person could give an inexpensive gift related to that class with a note saying I have paid for so many lessons or I'm contribuiting this much. They could even get a gift certificate from the school.
And I also liked the idea of telling them what your children's interest are so that they can give appropriate gifts.
If your family usually co-operates together I would think that a general discussion including these points could work.