Maybe Google is prompting you to uninstall? No I don't think it's because of your tab being root... Maybe unchecking Verify Apps will stop Google from prompting you... I hope this helps!
What problems are you having? (Remember, every app that you had before rooting will work exactly the same after rooting. Rooting doesn't change how the apps work, it just allows those apps that ask for root access to get it.)
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