I would strongly suggest that you get some outside help as you bring your two families together. It is extremely difficult to do that on your own, and for some people, it is impossible. If you can afford professional counseling from a marriage, family, and child counselor who has dealt with blended families, it would be wise to get that assistance. A pastor also might be able to guide you, although there are some tough relationship issues to be handled by a professional who has "been there" before.
You're already experiencing the thorny issue of conflict between Bill and your children, which is common. One of the kids is likely to see him as a usurper. When a mother or father dies or when a divorce occurs, one child often moves into the power vacuum left by the departing parent. That youngster becomes the surrogate spouse. I'm not referring to sexual matters. Rather, that boy or girl becomes more mature than his or her years and relates to the remaining parent more as a peer. The status that comes with that supportive role is very seductive, and he or she is usually unwilling to give it up. The stepfather becomes a threat to that child. Much work must be done to bring them together.
The kids' loyalty to the memory of their dad is another issue that requires sensitive handling. In their eyes, to welcome the newcomer with open arms would be an act of betrayal. That's certainly understandable and something that must be worked through with your children. It will require time, patience, understanding, and prayer.
I would say the greatest problem you will face, however, is the way you and Bill will feel about your kids. Each of you is irrationally committed to your own, and you're merely acquainted with the others. When fights and insults occur between the two sets of children, you will be tempted to be partial to those you brought into the world, and Bill will probably favor his own flesh and blood. The natural tendency is to let the blended family dissolve into armed camps--us against them. If the kids sense any tension between you and Bill over their clashes, they will exploit and exaggerate it to gain power over the other children, etc. Unless there are some ways to ventilate these issues and work through them, battles will occur that will be remembered for a lifetime.
I have painted a worst-case scenario in order to prepare you for what could occur. Now let me encourage you. Many of these problems can be anticipated and lessened. Others can be avoided altogether. It is possible to blend families successfully, and millions have done it. But the task is difficult, and you will need some help in pulling it off.
The Apostle Paul wrote, "I have fought the good fight, I have finished the race, I have kept the faith." (2 Timothy 4:7) Dr. James Dobson chats with Pat Robertson, who has been fighting the good fight as a TV evangelist since 1960. Pat talks about starting Regent University and the Christian Broadcasting Network, along with his 1988 presidential run, the combative world we live in today and the hope for a Third Great Awakening.All Sermons by Dr. Dobson