How can I Keep my Dogs from Squabbling?
The key point of your question is that the fighting occurs when one of the dogs is receiving attention from you.
Dogs and people see the world from different perspectives. Humans generally favor equality. If we have two dogs, our idea of fairness is to treat them as equals. We give them equal amounts of attention, love and kindness.
Dogs, however, are not proponents of equality. They establish dominance hierarchies among themselves. In a pair of dogs, one is likely to be dominant. The other will be submissive. In the dog world, the dominant dog has first rights to toys, food and attention from the people in the house.
As long as the submissive dog respects this entitlement, peace will reign. However, some submissive dogs realize that they can challenge their dominant sibling by enlisting an ally: a person in the house. The submissive dog may fail to respect the dominance of his cohort when he knows that mom will back him up. The dominant dog responds by starting a fight.
The key to ending these fights is to realize which of your dogs is dominant. The dominant dog should be the first to receive attention, food and toys.
I am not saying to neglect the submissive dog. However, if you look at the situation from a dog's point of view, your life may become more tranquil.