Wow, I was a little surprised too. It seems that Google won't allow Gmail to be embedded or framed into a web page.
Forcing whatever code is making it take over into stopping is beyond my power. In the mean time, can you make it open into a new tab or page? Even though that won't be as convenient, it looks like it's your only option. If you're dead set on getting it to fit into your own website, I hope this post will catch the attention of real professionals that can help you. Sorry I couldn't be of any help.
Also, when you're asking for help on this sort of thing, make sure it goes into the General Discussion & Help section.