I just read through this thread of your sitch, I know that all the changes in the last month are a lot to handle, but you seem to have your head on straight and are steadily moving forward.
Based on what I read, I definitely think you will be best served in holding off on dating for a bit. There is a lot of your W in your posts, and I suspect you still have a long way to go in being truly detached. I know when I physically separated, I spent 3 or 4 months full of emotion, and if I was to go back through my thread, was probably saying I was detached at the time. Even though you've been nesting, it's different than when you actually have two homes, you start to build a life that the other person isn't involved in, that's when I found my independence starting come in leaps and bounds.
Congratulations on getting to keep the family home, I know there are memories of her that will take a little time to get past, but there are also memories with your kids that are irreplaceable. I think one of the things I miss the most of my past is getting to go into my sons room every morning to wake him up. btw, do you have someplace in the house that you mark the kids heights with the dates? My son liked it (we did it on the doorframe to his closet), especially being able to see the growth spurt that hit around 12.
Also, don't feel like you have to leave the newcomers forum, there is a lot more traffic here, but of course you're welcome to post wherever you feel most comfortable.
M - 9 1/2 years 5/5/16 - Bomb drop - 3 week EA 10/31/16 - We sold house 01/10/18 - D Finalized