I understand you Theoretical. Here are a few thoughts.

An effort to comfort someone (or do anything for another person) should be freely chosen by you rather than coerced or pressured or requested by someone else such as your mother. She's actually overstepping there. How you relate to your cousin after a death or anyone in any situation is entirely up to you.

So the question is, do you have a desire to call up your cousin and try to comfort him/her.....regardless of what your mother wants?

All that matters is what YOU want to do. Assuming you are not a parent, your only responsibility is to yourself. Other people need to figure out their own lives. If you had a spontaneous desire to help someone else, that's great. If not, no problem...don't do it.

Does that make sense?

Nothing wrong with simply sending a sympathy card...shows respect and care. If you want to. Doesn't have to be a phone call.