My spouse and I both laugh about how when we got married, in our 20s, his mom showed up with whatever of his possessions he had left in her house, like the day after we got married. I already had my stuff because it had also been made clear to me that I was expected to take it as soon as I no longer lived in a dorm. Whether or not I had room for it was not my parents' concern!
Our parents were not shrinking violets when it came to having ideas about getting our stuff out of their homes! Which I respected, to be honest. And why have stuff if I didn't have it with me!
I wish you luck with your kids' belongings and remember, there's always 1-800-GOT-JUNK. They do the lifting for you. :)