There was a reason for my question. You raised the issue of nutritional deficiencies; if the children had specific diagnoses requiring specific medical treatment and dietary requirements, you may have had a point about Mom feeding them junk food. That does not appear to be the case, given that you've said both children were born very small to begin with....and I'm sure if there was a firm diagnosis you would have mentioned it. Being in the lower percentile of their age group does not necessarily indicate there is a medical issue.

Bottom line is that no matter how much you dislike it, Mom is legally allowed to visit the kids during the school lunch break. Even during "your" days.