Once your mother is satisfied that her new phone is set up correctly, and that her data transferred, this is what she needs to do to prepare her old phone for you:
What to do before you sell, give away, or trade in your iPhone or iPad - Apple Support
You can then follow this procedure to transfer your data from your old phone:
Use Quick Start to transfer data to a new iPhone or iPad - Apple Support
If you have any music on your old phone that was purchased somewhere other than the iTunes Store (e.g., it's from your own CDs), it won't transfer. You'll need to load the music onto the iPhone 11 from your Mac or PC in the same way that you originally loaded it onto your SE.
Once you're satisfied that everything transferred properly to the iPhone 11, if you want to get rid of the iPhone SE, follow the procedures outlined in the first Support article.