If it makes you feel better (or worse) I plan on eating pizza Christmas Eve, per the usual.
(a tradition started when my grandma got sick the first time)
and then opening my ratty misspelled Christmas stocking 
Why yes, it does make me feel better.
I once read in one of those women's magazines that the consistency of the traditions can be more important than the traditions itself. I believe the author encouraged people to quit knocking themselves out for the holidays. "If all you do is heat up a frozen pizza on Christmas Eve, your kids will someday feel nostalgic over their Christmas Eve frozen pizza!"
Maybe there's some truth to that one.
There's definitely some truth to that one! When I was a kid, every year my mom bought us each a box of those chocolate covered cherries for our stockings. I'll be 25 this Christmas, haven't lived at home for about 7 years, and I don't even really like those cherries anymore, but it's still not Christmas for me without them.
OP, with the added information, I definitely think that the stockings aren't where you should start. Once you've gotten halfway to Martha Stewartness, then you can reassess the stockings, as your mother will already have seen that you're serious about this and it isn't just about her stockings. An earlier poster also made an excellent point about the lesson this will teach your girls, and it's important to consider that. As far as the girls' opinions go, I don't think you should do anything that they aren't fully happy with. Normally I wouldn't suggest letting the kids do whatever they want, but I think they have the final say in this, and they shouldn't be forced to compromise. My homemade stocking is nicely done (just red, green, and white crocheted granny squares in stocking shape), and it was made for me by one of my father's brothers. Now that neither of them is alive, my stocking serves as a link to both of them. I would never give it up, no matter who wanted me to replace it. Your girls may one day feel the same way.