As far as I know you can't have an Israeli stamp in your passport. If you get a second passport that is free of Israeli stamps you will be fine. I think lots of businesspeople who need to travel all over the Middle East including Israel use the two-passport technique to avoid problems.
It doesn't really help you because you already have a stamp but for future reference you can ask the Isreal visa office to stamp on a seperate paper, they'll do it and when you are done travelling "lose" that paper.
You should check with the UAE consulate but i'm actually pretty sure you can get into the UAE with an Israeli stamp.
dont worry about it. Technically its not allowed, but they dont care. I know of a filipina who had a one page israeli visa on her passport and the UAE immigration stamped the entry stamp right on the opposite page of the passport.
The only countries who are still really strict about this are Saudia Arabia, Syria and Lebanon.
I think it wont be permitted,if u have a new passport too,governments are not stupid,Uae will know that u had a israil visa on ur passport,informations will be stored on comp. systems.