Again, you are confusing Apple ID with iCloud account.
I think I see e difference now but are you sure that an iCloud account is a an email address that ends in .me?
No, it ends in @me.com for example, [email protected]
I am definitely using my gmail ID as my iCloud account I can see that by going into settings on my iPad.
No you are not! When, or if, you set up an iCloud account (formally MobileMe) your are setting up an account that is used for the services that are delivered by that service which includes email, calendar, address book, iChat, FaceTime, iMessage, Photo Stream, etc.
As podgirl posted above you can turn off or not use all the services of an iCloud account but if you share it with another person you will experience conflicts with certain ones namely, email, iChat, FaceTime, iMessage etc.
Now, that's not to say that the email account that your are accessing from your iPad is not your Gmail account, it is just not your iCloud account. You may not even have an iCloud account for all I know.
Once you've created an iCloud account you can use that as an Apple ID but then again you can use any email account you own as an Apple ID, including the Gmail account you already have. It does not need to be an iCloud account.
I also don't see what email has to do with this if you are using non-Apple email such as gmail or yahoo. If my wife and I are using the exact same Apple ID for everything I can see how it would cause problems for iMessage, FaceTime, etc, but I don't see how it would have anyone to do with her Yahoo mail getting crossed with my Gmail.
You are correct your Gmail account and your wife's Yahoo account are separate and I never suggested that they would interfere with each other. iMessage or FaceTime on the other hand are iCloud services not Apple ID services. If you are both sharing an Apple ID that is not an iCloud account then you won't have any conflicts regarding services that are iCloud based.
My point is that an Apple ID can be registered using any of those email addresses it does not have to be an iCloud account. If however you want to share apps, movie/TV purchases etc., between the two of you it would be best to use one Apple ID for both of you and that Apple ID can be any ID you choose.
I've said the same thing three time in three different ways. If you don't understand by now I'm afraid that demonstrating the difference while standing over your shoulder is the only other way I will get through. And that ain't gonna happen, sorry.