Sounds like she's manipulating you and your brother through guilt. And you're letting her, which means weak boundaries in the relationship. Everyone has feelings and emotions that are sometimes unpleasant to deal with, but you giving up what you would like to do for her sake, her wishes, her loneliness that is ultimately enabling this behavior to continue.

I say support her in ways that you are comfortable with when you're comfortable doing it, but do not let her dictate to you when you must be there or she is just controlling you. You come first in your life, then you have the strength to help others, not the other way around.

Talk to your Tdoc about this, regarding boundaries.
Good Luck