I guess I don't understand why opening them early is even an option. It's kind of like saying, "I've done my shopping, the gifts are wrapped and under the tree, so the kids might as well open them now" If you really want them to open gifts early so that they aren't overwhelmed on Christmas, I would suggest letting them open the gifts from you because your mom specifically asked to have them wait.
You could also spread it out saving some gifts for after Christmas. Maybe open a present a day after Christmas until New Year's Eve. That could be fun
We have family all over the country, thus, we, too, get boxes. We've never opened them before Christmas. We don't even remove them from the postage box until Christmas.
A lot of the fun with Christmas and presents is the anticipation of opening them. I would wait until Christmas even if your mom didn't ask you to just for that reason. We get a lot of out of town gifts mailed too and always wait for Christmas.