In my group, we've been working with the understanding that you can wear a shield and fight with a two-handed weapon, the assumption being that you only get the +2 AC if you're actively wielding the shield with 1 hand. We're treating "wielding" a shield as different from "wearing" a shield. When you wield the shield, you need to use 1 hand for it, and when you only just wear it your hand is free to do what you like (cast spells even). In short, it allows us to use versatile weapons with a shield easily and change our strategy during battle without taking the 1 action to don or doff the shield. In one turn I can strike with 1 hand and wield the shield and in another turn I can switch to two hands for great weapon feat damage, losing the AC but gaining a lot of damage. We think this might be reasonably balanced because we can only modify our AC during our turn until our next turn, so we're not allowed to strike with two hands and then switch back to wielding the shield in the same turn.
Another reason we may have used this "rule" is because you are allowed to equip a weapon as part of the attack action, as stated in the PHB (it's not with me at the moment).
Is there a rule in the PHB or somewhere else that allows this kind of interaction, or have we made the whole thing up out of convenience? Can a shield-holding hand do anything but hold the shield?