New here...and I need some help...

I will try not to make this too long...some background... most of my family has passed away. Mother, Father, and six years ago my sister who I was very close to. I am the youngest in my family and I have just two remaining brothers left in my immediate family, one whom doesn't contact anyone anymore and hasn't for a long time.

When my sister passed away she made me executor and had within the last year of her life changed her beneficiaries on her life insurance and IRA accounts from splitting it between my two brothers and I to removing them and leaving all of those to me (she did split between the three of us her estate though). I understood why she did, because neither of them had contacted her in that last year of her life (until the end) to even see how she was. I did not think it would be right to not split up the money so I split it with them anyway (except for the IRA which was way to complicated to split). The reason I explain this is because when I arrived back home after the funeral, and handling her estate my brother and sister in-law became agitated with me, picking fights, ignoring calls and texts. I tried to reach out to them on many occasions to try and straighten out whatever was going on, because honestly, I didn't really know, I just assumed it had to do with how my sister had left things, that they were bitter, even though I split the money with them when I did not have to...each time they claimed they were not angry with me and got very defensive "where would I get that idea from?" as obvious as it was... after many attempts at reaching out I finally left it alone, I thought time would repair things, but it didn't. In the past couple of years I have thought that I was closer to accepting that they did not want any part of my life but recently I realized I was not any further along emotionally. I found out that my nephew (their son) got married and they never invited me...I was left out. I guess this was the nail in the cross that showed up for me that made me break down these past couple of weeks realizing that they really don't want me in their lives. It has been hard. I think I held onto false hope for way too long.

My question is for anyone who has been through anything similar where you finally had to admit there was no hope and that the best thing is to move on from your family...how did you do it? I have no hatred for them, and amazingly no anger either (maybe I haven't reached that phase yet even after 6 years) so all that sits within me is hurt and sadness....how do I let go of this forever? How do I accept this and move on? They have given me every reason to do so, why does it seem so impossible for me to walk away?