Yo M......I read that one of the signs that indicate if your ready to date or not is if you are no longer angry at your W/H. The same article also indicated that another indication is if you have acknowledged and accepted your role in the relationship and your contribution to the failure of it.
It's good to hear that you are processing your emotions especially for your kids. It will be a huge benefit to them if they see mommy and daddy interacting positively. Especially when it comes to Birthday's, Mothers Day/Fathers Day, etc.
It was my EW's birthday yesterday so I took the girls out shopping so they could get her a few little things to give to her, along with a small cake and a card (they had been asking me for weeks). They asked me what I got her and I told them the presents we got where from all of us.
So she came over to the house and we did the birthday thing for about 20 min and then she left.
I was just happy that I was in a good place emotionally to do this for my girls.