It’s really awful and very upsetting I know OP 
We we’re in a very similar situation a few years back, as we decided to relocate as a family, only difference was our DS’ were grown up by this point, we all idolised MIL (now unfortunately late MIL) she was a wonderful person and helped us so much when our DS’ were little. We were very, very close.
We had very specific reasons why we decided to move, mainly surrounding my disability, financial, better city/opportunities for our DS’ etc. we had tears, and a lot of emotional moments before and after we moved. It was a really horrible time.
But we did move, 3+hrs from where we used to live. And it really has been the right decision for our family, our only regret was that the move upset late MIL. But there were some other circumstances and many other family members around MIL. It did cause a lot of feelings of resentment at the time, I will be honest.
But MIL will come round to it in time, once you have moved, she will have to come to terms with your choice. It’s totally wrong to try and emotionally blackmail. The distance you are moving, is not that far, it allows for days trips, it’s not Australia. Yes, it’s a change, but you need to do what’s right for you.
My DS’ girlfriend (currently at uni in our city) hails from a very long distance from us, who knows if he may end up moving back with her, but that is his choice. We would be sad, but I wouldn’t tell him or let it show. He needs to live his life.
Wishing you all the very best OP
but you must do what you need to do. Good luck.