Does your mother have her own MDE account, and is listed in your sister's F&F list? If so, the procedure in post #2 will work fine.
However, if your mother does not have her own MDE account, then your mother's profile exists only in your sister's MDE account (and is "managed" by your sister), and you'll have to use a slightly different process and go through your sister to link your mom to your MDE.
Is your sister already linked to your MDE account in your F&F list? If so, navigate to the Add A Guest button as above, then click Find Through My Connected Guests, and then your mom's name should pop up. Click the box and follow the prompts (I can't remember what you need to do - it's been a while for me). That will link your mom's profile in your sister's MDE to your MDE, and you'll be able to make plans for her, book LLs, etc. Her MB will be linked to that same profile so it will work at the park gates, LL entrances, etc.
If your sister is not already linked to your MDE F&F, you'll need to add her first, then add your mom through her.