@bdipti,
I don't know how long you have been going out with this man for, or whether you were even the cause as they tend to lay on you, for his seperation but he does have a responsibility in my opinion, to do "something" ... And to me, that is not to tell you where the door is if you are not happy but to work out how to make this more comfortable all round as he is not even Divorced yet.. He is still married.
If you do not like her messages to you, change your mobile telephone number, there is no need to speak with you, he attends their marital home to see his children.
The children in my opinion at this point in time should not be subjected to get along with you at all, rather, to see their Father and have some peace until they get used to the idea that their Mother and Father no longer live together and are Divorced. They are not at that point yet.
I would just concentrate on your relationship with your new partner at this point and suggest the same to him. In time, when they get their heads around things, and you are still in the picture, they will slowly get to know you.
My step-daughter was 11. She accepted me. But I refused for my now fiance to introduce me to her for quite some time.. And, I certainly don't act like a step-mother to her now, rather a sister, unless I'm in a cheeky mood and pretend I can send her to her bedroom...
Bottom line is, this is to fresh and raw by all accounts. The ink hasn't even settled on any paperwork yet.