Well, we went to the park together tonight. Luke was ignored for the most part but he's a little hard to ignore entirely even for a sulking big Berner. He frolicked like a spring lamb in the mud grass and discovered a patch of snow to stomp and dig in.
Maya tried her hardest to turn her back everytime he approached. I can't tell if she is afraid of him or in utter horror at this creature bounding about. Liam is much more tolerant and is trying to teach him in a different way. Luke strutted up to him intending to take the beloved frisbee--Liam gave him a powerful warning growl and Luke yelped in fear, stepped back, and looked wide-eyed. I tried not to laugh but he had been tugging at Liam's ears, nipped at the cat, peed on the floor, swatted Maya's nose, and went after my shoe in the span of 2 minutes! He was, shall we say, a bit demur after the correction.
He is now permitted to be a few feet near during naptime. He watches Maya closely and when she grooms, he makes an attempt as well. It's adorable how much he wants to be a big dog and mimics the other two but being accepted rather than just tolerated is going to take some time I think.