Can you get an annulment with a divorce?

I am a devout Muslim and I want both a formal divorce and a Faskh from her, or annulment. She has cheated on me and disgraced both of our families. I also want full custody of my daughter and son, I do not want them around the man she is now seeing. Can I get the annulment at the same time as I get divorced, and can I prohibit her from taking my children around another man?