markvii is absolutely spot on. the chimney is far too short in relation to the roof. the building is competing with the chimney for draft, and with an outside chimney, it's almost winning, hence the meager draft. Trees arn't the issue, don't waste your time with them. If you want to stop playing around, the solution is to bring that chimney about a foot higher than the peak of that roof to the left in the pics, be sure to leave the tile liner sticking up about 6" higher than that- above the crown and TAPER the crown nicely away from the tile (or just buy a precast crown at any masonry supply house that has the proper taper). Then 45º that pipe coming off the boiler and put that T with a baro in the body of the pipe, get the baro out of it's current location.