Thinking of you, OP. I am 6 years ahead of you and it took time, but I am much happier now. I still miss being married and in a relationship but I don't miss him one little bit. 22 years together and my feelings have changed from unbearable sadness to anger and quite a lot of bitterness to not giving a toss.
ExH left the day I found out about the OW. I couldn't bear to look at him. He 'loved her' and had been 'plucking up courage to leave,' apparently but still lied and lied and minimised to assuage his guilty conscience and make it my fault.
Children are very resilient. So long as you ensure that they know they are not to blame and allow them to continue loving you both, despite your feelings, they will be OK.
I would be as honest with them as is appropriate for their age. They are allowed to know you are upset and why.
Look after yourself, try to get as much RL support as possible. Some of my friends have been fantastic, others less so but they have been my lifeline.
Make sure you get help to complete your course. I had been a SAHM for 9 years and my career had been sacrificed for my exH's. Our middle DS has ASD and needed me to be there for him when he was young, but I've had to find better paid work to fit around school to support myself and still be there for DS2. ExH does pay maintenance but that only lasts until they leave school.
I lost shed loads of weight, the only silver lining, but have gained it back recently, a sign I'm back to normal.
So do try to eat.
The kids will help you get through each day, because you have to for their sake. 