He is adamant there is nobody else.. They always are. 
I’m so sorry for you. I hope for your sake that it is just a blip and that with a bit of time to think he will sort himself out. Unfortunately the most likely scenario is that he does have someone else and he is “messed up” trying to keep a secret. Don’t be surprised if he suddenly ‘meets’ the love of his life in the next couple of months, she’s been waiting in the wings for the coast to be clear.
I’m sorry to sound so harsh, I just don’t want you wondering what you could have done differently to keep him, where were the warning signs? Etc. Chances are he has been pondering this for quite some time and is only now landing it on you now that he’s sure.
Let him have his space. Don’t pander to him in the meantime. Give him the full force of ‘divorced dad’ life i.e. no cosy family dinners or him popping in to tuck them in at night etc. It will be confusing for the dcs (as well as you) for him to be in this limbo of living elsewhere but still being there when he chooses. Put some structure around this time for all your sakes.
Sort out how you will split childcare, finances etc. Be brutal about it. Even if it’s just a temporary split you need to be secure in your home and he needs to contribute fairly to the children’s lives, both financially and in terms of time.
If he’s really just after some free time and a taste of the single life, 50/50 childcare will no doubt come as a huge shock to him. Meanwhile you can take some time to yourself, nights out with friends and family, free time to go to the gym or hobbies etc. Make the most of the opportunity to be a single parent (I highly recommend it!) and let him see that he is not the centre of your world and you’ll be fine without him. Even if you don’t believe that yourself, let him see it.
Either he’s had his head turned and you’ve lost him anyway, or he’s hedging his bets hoping for something better than the family he helped to create, so let him see that he doesn’t get to walk away and live a carefree bachelor life, he can be the lone parent half the time too, dealing with homework, clubs, childcare, cooking, washing and all the shitwork that you’ve no doubt been doing for the past 8 years.
Sending you lots of love 