We don't understand your issue. Are you saying that with RealPlayer installed, YouTube won't play in your web browser?
We have not heard of this issue with anyone else and more over RealPlayer and YouTube on a web browser have no connection between them. Therefore, please confirm the following:
1. How are you using YouTube?
2. Which web browser are you using?
3. What version of RealPlayer do you have?
4. What is the Windows O/S version?