Bully Gander / No Eggs Problem

First, try to stop thinking of your birds' behavior in terms of human emotion. This bird is not a "bully", his behavior is a normal consequence of the inappropriate situation he is in, through no fault of his own. That often manifests as what some humans think of as abnormal behavior.
Three ganders with three geese (the correct plural of goose) is much too high of a sex ratio. In reality only one gander is needed in a flock of that size. You may try two, but there may still be some problems with even that. I understand that it is one of the females that seems to be bothered, but like I said, an abnormal situation is likely to produce what you interpret as abnormal results. It may in fact be the favorite hen of the dominant gander that is pushing away this hen. And are you sure that it is in fact a hen? You could try to take out one or two of the ganders. Two ganders without the influence of any hens can actually get along quite well, if they are out of sight of the hens. You could also seperate the six birds into three pairs, which would almost certainly solve the problem, again, if the submissive bird is indeed a hen. If any of that is inconvenient, remember that animals do not recognize your wishes. Their behavior can be modified to a certain extent, but that only goes so far if you do not understand and allow for their normal behavior.

Geese need very little shelter even in the worst climate. They can and will use a shed, but are more likely not to. Depending on what your pen is like, they may already be laying somewhere else outside. Look closely. Locking them in will not "traumatize" them, (again, human emotions), but they obviously prefer not to use it. You could also try just putting the A frames outside by themselves. They don't usually require elaborate nesting facilities. The shed is more for your benefit, or maybe to keep feed dry. Sometimes they might never go inside except to lay, or if that is where the feeders are kept.