I feel HOH would be a hard sell for her.  She lives in a friend's home.  The person is un-related to her children.  That person is filing HOH with her children.  My main concern is that she is eligible for EIC since her husband is a non-resident.  On the EIC info page it says that he needs to be a resident alien or a cititzen to qualify for the EIC if they file together, but I do not see anything if they file separate.