I somehow doubt BitDefender made their AV to be compatible with other AVs, whether it is actively scanning or not. Even if it was, Avast! is not. As Pondus said, read the link Donovansrb10 posted.
And uninstalling any AV product with some 3rd party tool can always go bad.....use normal uninstall or the company's removal tool (or both).
I could go off on IObit, but Pondus already presented enough relevant info about that.
At this point, I would first run the BitDefender removal tool appropriate to the version you had. Then if Avast! is still messed up, do a program repair. Thats done by starting to uninstall Avast! normally via Windows but choose the Repair option when it presents itself.