So long as you have other people in your life, lots of family & friends, why let this bother you. I agree, it is kinda childish of HER to not accept you again-if you have asked once you got back together with her son. Not everyone forgives & accepts again so easily. I have found in my life, women are the worst in this area.
I have a step sister, been friends since BIRTH, over the most mindless things, will delete me from her facebook (the last thing had nothing at all to do between me & her but something I did with other friends), so I let her do her thing. It is a little annoying but I am used to this behavior by now.
So I just go on with my life, when I see her out & about, I am genuinely glad to see her, and pretty much act the same towards her. And she always ends up coming back around to me, starts calling again.
I refuse to be offended by people who are too sensitve and have trouble with forgiving & accepting when we did little to nothing to hurt them. If we did, we need to apologize & put outselves out there . (only you know if this needs done somewhere in your life with your MIL ?? )
Life is too short. Some you will never please. You must look at this --as more of a reflection of who they are. Be kind in spite of it , love & care for her son and ... likely SHE will come around.