Can I amend my tax return on Turbo Tax if I didn't file on Turbo Tax

I think you mean you claimed yourself on your return instead of saying you can be claimed on someone else's return.  And your mother's return was rejected.  First of all your mother has to mail her return this year even if you amend yours.

To amend a return you did somewhere else, you would first have to fill out Turbo Tax like you are doing the original return and pay for it.  You have to recreate the actual wrong original return.  Then when it matches each line that you really filed you have to tell it you will mail it so it thinks it was filed.  Then you can amend it.

How to amend a 2016 Online return      https://ttlc.intuit.com/questions/3402261-how-do-i-amend-my-2016-turbotax-online-return

Can I redo my taxes if I did them on free USAtax