It seems you have a choice in whether the kids see their father, or not.
You are conflicted. You want them to "know" their father, and yet, not to absorb too much Islamic influence from him.
Might you simply not play the "sole" custody card and not let them stay with their dad?
On the other hand, just be sure to give them a good Orthodox upbringing. Perhaps you have to work on it a bit harder than others. However, teach them about Christ, Church, etc....so, that they not only know about their Faith, but, LOVE it!
Remember, to keep the Church at home, as well. Pray at home, talk about God at home, etc.
The best way to protect them from Islam, is to build a strong knowledge and love of Orthodoxy in them. Be gentle, but, be firm.
PS. THIS is another great example of why "mixed" marriages do not work.