Is this your 4th dog? Maybe it's one too many. My cats are like that. If you have to make it work, try walking these two dogs together, as Blanketback mentioned, get them on neutral territory. You said your new dog loves to be picked up? That could bring out some jealousy, maybe do that less and have the new dog next to you but not on your lap.
My dog is happy to share me with other dogs, but there is a fine line between petting them and giving them attention and having them too close, then she acts jealous or protective.