So I make a point of dedicating time for both Lily and Jamie to have snuggle time with Patrick. This does not stop the arguing and whining. But at least I can say I tried.
Jamison's snuggle time has to be very supervised. He has minimal concept of the following vocabulary words and phrases: be gentle, nicely, not so rough, don't pat so hard, remove your thumb from Patrick's mouth, and do not poke him in the eye. As he does this last one he is talking in high pitched, sing-songy voice - "hi cutie, how are you sweetie? i'm going to put my finger in your eye now, ok cutie pie?"
Whenever Jamie approaches Patrick there is an initial look of fear but then he relaxes and just goes with the flow.