You are experiencing a very valid and truthful state. You are feeling weak; you are wondering about all the rosy days of when you first met and got married.
You didn't want it to end up like this. And you are valid in your feelings about another woman parachuting in and being a second mother to your children; playing happy families and living the life you thought you'd have.
It's entirely legitimate and valid.
Be calm, by your own admission you've decided to separate and you've been getting on each other's nerves for years. This is a process. You need to separate your emotions from the practicalities of divorce.
It's not easy - I know. But take small steps. Remind yourself why you are separating. Write yourself a letter, as if you were writing to him, about all the reasons you are divorcing, any little moment however insignificant it may have seemed at the time; write it down.
It's a step by step process. Some women can go in guns-blazing over a divorce and others need a bit of time to process and reflect. You sound like you are in the latter group.
It's a rollercoaster - sometimes you will feel like you have wind beneath your wings and at others you will want to hide in a dark corner and avoid life.
All I can say is that these are all natural responses. You just get cracking. The longer the apathy, the longer the pain.
This is the end of the road and you must act. For your own sanity, if for nothing else.