I can completely relate to what you are feeling. I am also recently separated and in the process of getting a divorce. There are a few mutual friends who tried to contact us when we were in the phase of getting separated but our friends did not know at the time yet. My ex-husband told me that he will inform them. After that day I did not hear from those mutual friends once. I felt hurt that they did not feel the need to check on me and how I was doing. But as time is going by, I am realizing that this a part that comes with a divorce. Mutual friends are left with no choice but to pick a side. Some will pick yours, others will pick his.
All of this said & done, I think you are absolutely justified in feeling what you are feeling, particularly considering you know one of these friends since childhood. So don't be so hard on yourself. It is a natural human response.
Nonetheless, just remember that you cannot always control whose side mutual friends pick. So let things flow naturally.

I wish you all the very best. May you get the strength to deal with this difficult phase of life and come out stronger.

SushiNCorn