@Lyn20 Since one uses email (most of the time, unless you log in through Social Media: Facebook, etc.) to login it makes sense to me that your Mum can't log in if you changed the email to yours. Do you want to give your Mum the password to your email account?
(I wouldn't give my Mum my password! 🙂 ) I'd change it back to hers and then have her add you as co-host. That way you'll get to where you want to go (i.e. manage things) while she still remains the official host on Airbnb's records.
Or, she could simply de-activate her account and the listing and you set it up from scratch. You'd lose the reviews though.