Hurt...initially yes I think it will be tough for you, particularly being away from your children. I know because I've been in your shoes before. Thing is given the sitch with your W, it will benefit you greatly I believe to be clear of her. The time and distance will allow you to heal a great deal.
Having all of that "free time" to yourself...you may find for the first few weeks/months that you just exist, survive, read on here...heck maybe just eat and sleep although I would encourage you to work out/get to the gym as well. Bottom line you just have to make it through to start with. As you begin to see that your children are surviving the change...and they will even if it's not ideal...you will then feel more comfortable with and perhaps even cherish the time alone that you have for you to do with as you please, but that will take time to get to that place and then you might battle feelings of enjoying the free time vs not spending it with your children.
doing what you're doing is in my opinion a huge positive. let the OM full on have your W while you get clear of that dysfunction and work on yourself. i know it will be very difficult to be away from your children like that. don't discount the impact that it might have on your W being away from them for that long as well. this change will bring a consequence to her actions and who knows how that might affect her.
be strong H! know that you did not want this, these decisions are not of your control, but they are your life. you will have much time to get in touch with your spiritual side and have some peace on what is happening. as i say you just want to focus on making it through one day to the next. also one point of advice. when you stop and see your kids during the time you don't have them, DO NOT become upset if they don't engage you fully when you stop by. When I go to see my D4, it's not like we hug/love on each other the whole time I'm there. they are little, they want to play, perhaps sleep, perhaps fuss, whatever. just be thankful for the time you can see them even if it's only to kiss them, hug them and tell them you love them.