It usually goes that way, trouble never comes alone, when it strikes it multiplies and thus multiplied they hit you on several life fields. If you feel really lost, alone and disoriented can you find a therapist or some support groups? Actually I understood you already have a therapist, but maybe support groups would work better for you..
Sometimes it is hard to understand how partners feel in relationships with us even when they are our best friends. Do they feel, even when they love us as human beings, that we do some things they experience as obstacles in their personal growth? While it could be nice to preserve a best friend status while making pause in general relationship, some people need a complete distance to help them realize how they really feel. And that can hurt, I know. An honest talk should solve most of the problems, but if you tried and it doesn't and one of you is refusing a couple therapy, then I think you should give both youself and that person as much space and time each of you need. If one of you decide to leave for good than it is better it happens earlier than you invest more time, love, energy into something that won't work. And also feel free to find a new love instead of waiting too long for your partner to decide what they want. The risk of losing you was something they were willing to prepare for the first moment they decided to completely distance themselves. And I think that is OK, no matter how hurtful it may sound, I would accept it.
If I were you and if I had financial possibilities I would do something nice for myself and my kids and a dog. I would take a trip, or would organize frequent one day get-aways, had fun with them. Things like that. While working at the same time on introspection, just as your partner. It will be better, don't worry.
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Someone wrote in their signature English is not their first language. Same here.