It is an acceptable practice to sign the names of children on greeting cards and other informal forms of correspondence sent by a family.
However, it is not appropriate to sign the names of adult or married children to any form of correspondence. At this point in their lives, they should take on the responsibility of sending their own cards and correspondence.
Mothers, no matter how much you want to continue to include the entire family in your affairs, you must let go at some point. I was recently most humiliated for my mother-in-law when she signed both of her son’s and spouse’s names to a sympathy card sent to the father of my best friend without my knowledge. Luckily, the recipients realized she did not understand what she had done, but it still placed her children in an awkward position.