Many times, the man you fall in love with, has an ex and kids. Most probably you will accept the children and will make all possible for them to like you. But together with them it will get in to your life the ex too.
Avoid to be competitive. In this situations women tend to ask them self if the ex was more beautiful or smarter. It is very important to get over it. Ask your ex about his ex relation, about what went good and what went wrong.
It is very probably to find out that at one point their relation went on because of the kids and the fear of change.
A woman who falls in love with a man who has already kids has to understand that his happiness depends very much of his children.
Be open with your partner. He doesn't have to feel obliged to hide from you even if he thinks he does it not to upset you.
Try to maintain a social contact with his ex. This doesn't mean you have to be best friends but short chats about social event will help you both feel less uncomfortable.
Offer him your help. If you see he is in a hurry to pick up his daughter do this for him if you have time. This doesn't mean you have to substitute her mother because she has one.