What’s the point of having children if you’re outsourcing their family?
Do children not need their mother to develop healthy relationships with the people in school?
Do they not need to know that their mothers both enjoy their time together and yes do miss them when they are away but ultimately want them to become independent?
Does kicking them out to a school where their love is conditional and comes from strangers make you a better parent because you now at least have a way to say out-of-sight-out-of-mind, giving yourself a safe detached bubble?
Sorry if this sounds harsh. I do not have children and if someday I do, I pray that I will be emotionally available to handle being a parent. It sounds like you are looking for a way out of being there for your family.
IMHO perhaps talking about your feelings with a licensed therapist would make more sense than finding a reason that G-d forbid sounds like it is promoting abandonment and/or neglectful parenting.
Surely you are not asking for that and I assume that you love your sons more than anything, but simply are having difficulty burdening the loss of them when they return to school. When they are home, is their company filling another unmet need when they are not around? Maybe there is part of you that is seeking fulfillment during the remainder of the year. Helping yourself in this direction may give you the confidence to see that you can in fact withstand the separation anxiety each year.
You can do it and your boys need you.