What is the process of tacking a storm trysail if the boat has dutchman reefing, do those lines get in the way?
You will not be able to fly a regular storm trysail with dutchman reefing. If for any of many reasons the wind goes from one tack to the other, the dutchman lines will be torn right out by the sail or the sheets. That's one of the reasons I prefer lazyjacks. I can pull my lazyjacks to the mast (and I do whenever I hoist the main, it's much easier that way) and that gets them out of the way of a Storm Trysail
If you have what used to be called a Swedish Trysail or a blade (a tall trysail with a very, very short foot) you might just be able to clear the clew of the trysail forward of the most forward dutchman line, but that's a very unusual sail and it would have to have two sheets, like a jib, to clear the dutchman lines - most trysails have two sheets anyway. And even then, I think the flogging of the sheets in really bad weather would tear out the dutchman.