Onit,
I'm so sorry that it's hard for you with your in laws, there really aren't any words 
Would your MIL meet you - just you and her - do you think? It might help you both establish your new normal. Explain to her that you understand that her loyalty is with LCB (sad but true) but that you have valued her in your life and that both you and the DC would like to have a relationship with PIL aside from that of LCB.
Don't even mention Christmas - it's emotive at the moment. But maybe arrange to go out for the day - walk in the woods, winter picnic etc.
I would just say that while it's absolutely fine to be factual with her about how you feel try to keep emotions to the bare minimum ie "I'd hate to think that we can't continue to see you" instead of "LCB is a fucking twat and I hate his guts, please don't abandon us"
((Hug))
yeah I know it's not the done thing but sometimes you need a hug