I'm divorced but kept my "married" last name so that it is the same as my daughter's. However, schools should be very used to this by now. A fairly large number of parents have different last names than their children. I am friends with two "blended" families who each have three different last names in their household.
Divorced women are no longer "Mrs. husband's name". Women who haven't taken their husband's name are not "Mrs." at all. "Ms." solves many of these problems. I'm just "S." to everyone, that avoids most problems.
You can use any name you choose for everything other than legal documents - driver's license, marriage licenses, taxes, wills, mortgages, etc., - as long as you aren't using an alias to commit fraud. When I worked as an HR Manager I was surprised how many people went by a name other than the legal one, that I saw on the documents they needed to supply me to verify their employability.
Added: Really? Being asked to be addressed as "Ms. Myown Name" would make "a mess of people uncomfortable? Not in my city. Here, no one would presume "Mrs." anything. Among all the families I know, those households with only one last name are a minority. My daughter's school would not have an issue at all with anyone's last name. And, "X's mom" is always an appropriate alternative ! :-)