My take on this, if a person can't accept you for you, they are not worth it.
I admire you for all that you are doing for the sake of love for your children.
My grandmother who is now 95 and has her wit still, divorced my 1st grandfather (I never knew him) to stay away from his abuse to her and her daughters,one being mine.
She had to survive and take care of her children, the man was an alcoholic, nice when sober but a monster when not.
Back in ther early 20's society frowned at a woman being divorced, even if there was abuse involved.
Grandma stood up to this, traveled to the city everyday to work in a sweat shop sewing shirts.
Her retired neighbor would watch my mom and aunt.
My great grandmother even was ashamed/embarrassed that my grandmother decided to have the courage to make it in life and no longer be abused. "Grandma, you rock "

It is so ridiculous when society frowns on divorce, would they rather see a woman, and yes ,it could be a man, be abused and also their offspring? So stupid

The tough part, is the way this woman looks at your situation and has no idea of what has taken place in your life, in my eyes (only my opinion) is a phoney.
The other thing that is difficult, is to want your kids to have their friends, and it sounds like they get along well, but have this block between this woman (can't think of the exact wording) which in turn you feel may affect your sons.
It is good if they learn the importance of love, not the material things, and it sounds like your boys already know that.
I wish I could tell you how to handle this situation, but we are all different, I would gradually start to distance myself from her, and in time if it affects the kids friendships, they will eventually find new friends.
Never, ever, feel ashamed of what you may not have, be proud and hold dear of what you do have, and most of all be proud of how you alone are keeping things together and taking care of your sons.
Be sure (and I'm sure you do) to always let the boys know how much you love them, talk with them, hug them daily, if they are old enough, you can let them know you are doing your best, for the love you have for them.
I wish you lots of love and luck with this.
DE
((((((((((((((( catgirl and family )))))))))))