It sounds like she is moving on but anything is possible. You may want to work on the relationship but that has to involve 2 people not 1. To give you words of encouragement, there are many children who are raised by one parents or separated parents and are just fine. The key is to provide them as much stability as possible, be as kind to each other as possible, show them love and that it isn't about them, and to have and spend quality time with them. As a loving father, you can probably do all of these things. Children don't benefit from seeing a dysfunctional relationship or a negative one.
As far as your girlfriend, I think she has already said I am moving on and also behaved as such. Her behavior alone says she is back playing the field and has begun to put her emotions elsewhere. Save yourself the heartache by moving on as well. You can always hold a small amount of hope regarding reuniting. But your energy needs to be spent figuring out how to separate on the best terms possible.
In addition, this is going to be an emotional time. Don't use this as an excuse to drink. That harms the children more than breaking up does. Find a solid and reliable place for your sobriety now such as AA - not when you are at your saddest.
The longer you stay listening to I love you's that don't matter is longer that you won't be living independently