Q:

Randomly Alternating GMs in D&D 5-e

Problem Setting
About two years ago, my life didn't allow free-time for reading fantasy literature and playing role-playing games. I miss it - I want to play D&D again.
However, life outside of gaming is still hectic, so I find it hard to pick a time and date for a gaming session in the future and stick to it. Thankfully, a cousin of mine (who actually introduced me to D&D in the first place) is also coming off an RPG hiatus and interested in forming a new D&D group. We've come up with the following way to solve this problem...
My GM-ing Idea
On any given gaming day, at least one of us will have the mental capacity to be the group's GM. So, our tentative plan is that unless we are absolutely certain of our schedules, we both prepare game plans prior to each gaming session. Come the gaming day, we privately decide who is more prepared and that person has the honor of being the GM that session: who is the GM is a game-time decision. The other GM would play their character.
Our group is generally fine with minor continuity issues arising from the author of the campaign's story changing randomly - in fact, our proof-of-concept mini-campaigns reveal it adds some much-appreciated comedy. We think that an "off-duty" GM playing a character is not game-breaking, since that GM is not aware of the other GM's game plans. We'll both GM the same campaign - same setting, same characters, same physical stuff - but the story-line and social developments in the campaign will inevitably come out differently than if one of us was a consistent GM.
Would it be easier if the "off-duty" GM plays the same character, so that character is always present in the group, or different characters? What bad experiences do you all have (that you know how to avoid) with randomly alternating GMs?

A:

Use split characters.
Different players will want to play different characters, which different choices. Whether its character creation (race, class), leveling (specialization, spell list), role-playing (aggressive, shy), you will want to do different things at different moments.
Eventually, one of you will do something that the other won't agree with, or will not play as they prefer to avoid offending someone. That makes the game less fun.
If you're worried about keeping up in terms of loot or level, when one of your characters levels up, the other off-line character also does. When you receive part of the loot, the other also does. This keeps both of you on par with the rest of the party. Being GMs, you can also compensate for inequalities (if any do arise) by clever loot or specific encounters.
The biggest reason to split characters will be 'player mistakes'. Let's say you are playing your shared Wizard. You play it safely, invest in offensive spells. The other guy is more reckless, and while you're DMing, he doesn't notice the obvious trap ahead, gets poisoned and shot to death by kobolds. Your character just died due to the other guy's mistakes. This can create a bad tension among both of you, as one feels frustrated and the other guilty (or not sorry at all).

As an example, I had a skeletal NPC once, Brooks. He didn't need to breathe and my players eventually went to explore an undersea sunken ship. The barbarian's player was moody and there wasn't much for the barbarian to do (no diving suit for him). So, I thought of giving him control of Brooks for this mission and go from there. The player nearly killed my NPC just from being pissed at low-rolls and crap loot, trying to use excuses as lawful good nature to have him nearly suicide to bring back skeletons of dead sailors. Despite just being an NPC, I was kinda mad at the player. Imagine if that were an actual character I'd put hours into, instead of just some NPC based on a manga. Btw, eventually we talked, worked things out, and he apologised.

There isn't usually any issue with alternating GM if they agree on a set of base rules.
Aside from the character-sharing issue, there should be no problems if you communicate properly. If you create something in your world, the other GM cannot just drop a meteor on it and destroy it. If the other guy designed a system of Deities with specific hierarchies, you cannot just create a supreme God that overrides them all. As long as you communicate the base rules of your world, there should be no issues.
Other problems that might still appear depend on the items given to the party as loot. Specifically, weird random strong items like the Deck of many Things, or the Wand of Wonder, can break games. You can either also discuss loot, or simply forbid the use of some items when it is your turn to GM.

For example, a friend is running a World of Warcraft-based campaign. In a night where he couldn't make it, I ran a one-shot based on D&Diesel and gave my players a baby steampunk-dragon. The dragon acts as a familiar now, as a pet from levels 5 to 10, as a mount from levels 10 to 15, and as a young dragon from levels 15 to 20. At least that's what I imagined. My friend, the original DM, wants no damn dragons in his campaign. It will ruin his plot hooks, plus make balanced encounters tougher, plus WoW dragons are vastly different from D&D ones. So he just banned the creature while he DMs. Players can use it when I'm running one-shots, but the rest of the time, the dragon just rests in the inn waiting for us.
As for world rules, I'm also alternating DMs in another campaign. To avoid world-rule intersections, we are having lots of dimension shifts from one to the other, so that each dimension has its own setting. On one, it's the usual fantasy D&D setting. On the other, we are in a broken world, where the earth has been ripped asunder with the fury of the gods. Once in a while, we also have a sort of flashback, where we run a one-shot on the other dimension as if it were just an old memory we were reliving.

A:

A buddy of mine did this back when we were in the military.  We had a huge three-ring binder (this was awhile ago) that we kept all of our notes in.
It allowed us to alternate and pick up/leave off where the previous GM ran.  It actually worked out really well for us since we had desperate schedules.  
My only cautionary piece of advice would be to ensure that alternating DM's can metagame player vs. character knowledge out of things.  

