I'm not sure what the issue is with your second cousin's Mother on a physical level.  I do know that when I'm sick, I have very little energy to talk with anybody and pretty much want to be left alone.  I also know that people who are dying have only so much energy and some will only allow a few people into their inner circle because of this lack of energy and their need to do what they need to do to let go and die.  Many of my loved ones to include friends have died or struggled through life threatening diseases.  Some have wanted me to be close to them.  Some have only wanted cards or e-mails.  Some have wanted prayers or to hear funny stories or to be read to or listened to.  Some haven't wanted me at their death beds.  Others have.  None of their choices had anything to do with me.  My job was to hear what they needed at those times and to give them what they asked me to give. 

If it your cousin who is tending to her Mom and is your cousin who is the one wanting only e-mails, etc - I know when my Dad was very sick and dying, I could only talk with a few people.  The rest of what I did was through e-mails or texts.  I needed to use my energy to deal with my Dad's needs, my sibs' behaviors, and the losses my Dad's death meant to me.  I didn't have the energy to listen to others or to be there for them.  I needed all my strength to be there for and with my Dad and my own children and grandson. 

Maybe some of my experiences will be a help to you?  Hope so.