I know exactly what you are talking about!
My problem is very similar. No matter what I try, it keeps asking me for the old account, unless I reinstall the app.
But even the reinstalled apps keep asking for the old account for an update.
Did you figure out where this old account is stored?
Chris, I tried your solution but it did not work for me. I have changed my email address/sign-in at the Apple site and in ITunes both but my IPhone and IPad will not pick up the new Apple ID and there is no way to change it anywhere. When I go into Settings, Store, and touch the Apple ID which has my old email address/sign-in still, there is nothing that comes up where I can edit it. A screen comes up with my Apple ID at the top (not changeable) with with four options as follows: 1. View Apple ID (all that does is once again take me to somewhere that once again wants my Apple ID password and it has my old email address/sign-in that cannot be changed). 2. Sign Out 3. IForgot (for a password that you forgot) and 4. Cancel.
In ITune when I click on Sign In it will bring up a screen where both the User Name and Password are blank and I can fill it in with my correct information. But I simply cannot get my IPhone and IPad changed and, therefore, cannot get into ITunes at all on either device. This is really getting frustrating. I contacted ITunes Support and they could not figure it out either and advised me to go to technical support which I will not do because I will not pay for technical support. Any other suggestions?