I have this set-up by accident with my ex-wife. It's correct that you would need to get the family account for the music.
Regarding other things, I think it is possible to run the two Echos on one account, as long as privacy is not an issue. The other person could I guess listen in to your Echo (I seem to remember this function - I may be wrong)
Any routines you set up you have the option to make device specific, as with alarms etc. However, I get nofications when my wife orders things on Amazon - not really a problem but you might not want that. Maybe there's a way to turn this off.
If your mother is elderly and not that tech savvy, you could help her by setting up alarms specific to her to put the bins out etc.
Simon