Is it advisable to run a campaign where the GM occasionally rotates to be a regular player while a player becomes the GM? I've seen some mentions of this strategy to prevent the GM from getting burned out from always planning, but it seems like having an alternative game going would almost be better. That way you don't have one GM giving out treasure beyond what the PCs should have and the other GM having to deal with it.
[RPG] Is it advisable to rotate the GM role between players
gm-techniquesround-robin-gmingsocial
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First and foremost it is important to me to mention that those of us that play this game for the story and as you say "correctly" (although it is a bit of a misnomer given that there is not an "incorrect" way of playing) the story of the character is and of itself its own reward.
I played an evil Halfling wizard once, for a single session. He was out for his own gain and in the pursuit of that somehow thwarted the assassination attempt on the rest of the party, to whom he had not yet been introduced. He ended up dying pursuing his goals. My reward for playing my character? There is a statue outside the library in honor of my "heroic" sacrifice for the lives of the others. I am touted as a hero, sort of like the Ballad of Jane from Firefly but this was way before I ever saw it.
Rewards I have used are:
Bonus XP: I usually don't do this anymore but it is an option and I know other DMs do this a lot. I will still give bonus XP out occasionally, but it is a bit tricky at times if the others slack too much and lag behind more than intended... so be careful with how much at a given level if you choose to use this option.
In game advantages: I have started to prefer this approach, in this way you gain tangible advantages by how you treat people and with whom you interact. This gives the world a feel of interconnectivity as well as realism, that what they do matters. If your other players are raping and pillaging and treating the NPCs like dirt they should expect to be treated with reciprocity and if they see that your ideal player is getting free room and board for saving a kid from a runaway wagon or offering to work in the kitchens, they might be inclined to switch tactics. On the converse if the evil characters that are the bullies are playing well you can have them be approached by contacts for them as a reward for that sort of thing.
Inspiration: Which you indicated in discussion that you already use judiciously but was removed as a discussion in the comments of the original post.
Some players drive the story others are along for the ride, by making his character the chief piece in a story is a good way to reward him as well as set the example.
What I would recommend is that whatever reward you decide on make sure it is available for everyone and everyone is told why they are given this or that reward. Even if you hand out XP for bonus and awesome play be sure to itemize that with what this piece was for and that piece. This allows them to see for them selves what their efforts glean.
Possibly, depends on a few specifics
What it sounds like you're doing is a style of railroading "Illusionism" (as pointed out by firedraco in the comments). This is essentially presenting a false choice in front of your players, when no real choice exists.
Why did I say possibly? Because there are a few specifics you can do when you run the game that make this method a time saving preparation tactic that doesn't invalidate choice.
For instance: If your players decide "Hey, that mansion we've found looks boring/scary/whatever, let's go down the other path," do you force them to stay at the mansion? Do you quickly swap fluff differences (Ok, the mansion is now a cave complex, the skeletons inside are now in the cave)? If the answer to these is yes, then you're definitely railroading.
On the other hand, if your players come upon the mansion and then they say "I don't want to go to the mansion" do you instead say "Ok guys, I need ten minutes to prepare the area down the other fork, you caught me with my pants down"? Then you aren't railroading, you're respecting their choice by allowing something meaningfully different to happen.
Blind Choice is no choice at all
That is to say; a choice between a road or a forest doesn't matter if there's no meaningful information about what lies upon the path or at the destination. Since it's a road or forest, you could easily say "Well, the road is well trafficked and speedy, but bandits hit there often. The forest is safer and has basically no risk of bandits, but there are weird creatures there..." Then you've provided the information to make said choice meaningful.
Players know
Oh yeah. Players get a sense for railroading when they're continually presented with blind choices, particularly blind choices that always lead to the next step in the "plot". They may not say anything because they're being polite, or they're enjoying the game anyway, or any other number of reasons. You aren't going to fool them, at least not for very long.
I highly recommend Courtney Campbell's series on the quantum ogre, the first one being here.
How to avoid railroading?
Well, some players don't actually mind railroading, at least not the nice kind that puts them on the plot where they feel involved and not the hamfisted kind that arbitrarily says "you can't do that". If your players are like this, you've really got not too much to worry about (except that they might expect you to provide all the life and effort, which will suck).
On to how to avoid railroading (Macro-Scale): Have an area map. Put a few cool things around the area, along the road, in the forest, whatever. When your group comes to the fork in the road, you'll know there's at least something along both paths to be interesting. Provide information about areas. A lake with an underwater city of evil frog men that invade the nearby villages can be as simple as a paragraph of description or less. Learning to be comfortable improvising off the bit of information linked to each area (and then adding that info to your notes) is one of the best things you can do to improve as a (non-railroady) DM. You don't need (or want) a prepared, defined plotline as a non-railroading DM, since plotlines are often easily destroyed or subverted by the whims of the players. This doesn't mean you can't have a loose plot with characters, just that it's going to get sent in wildly different directions when you let the players play and you'll have to not get attached to any specific direction.
(Mirco-scale): You say you include one puzzle and one combat encounter per area? Try making a small but non-linear dungeon instead. From The Alexandrian's Jaquaying the Dungeon: 
The lines are linear paths that can be taken (including lines of rooms + hallways). Note how the paths loop in on themselves, allowing for backtracking, exploration, and the ability to skip stuff. If your players are curious and engaged, they'll appreciate this ability to skip around encounters and puzzles, and they might even backtrack and explore when they don't have to. Don't be surprised if they don't, either, but missing content is part of the risk of free choice. If you need a boss encounter to happen, just put it as a linear path at the back of the dungeon, that all optional paths will connect to.
None of this is comprehensive, but hopefully this helps you out and gets your mind spinning with ideas.
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Best Answer
It's been a long time that I've played in a group where only one person ever GMed anything... As specific games rise and fall, usually someone else will run something sometime, unless they are a control freak or everyone else is totally slothful (this was the case when I was in high school, though, to be fair). But nowadays, we always have multiple concurrent campaigns going on with different GMs running them.
Rotating GMs within a campaign is different - to a degree, it depends on the nature of your campaign. I've run campaigns that are very coherent stories, with loads of secrets, that I'd never rotate in the middle of. If there's a concrete vision, you don't want to rotate. If there's less of one, it's easier - kinda the "Babylon 5 model" vs the "Star Trek model." So rotating within one actual campaign is possible but is more or less desirable depending on the type of campaign.
In one campaign we proactively said "Hey, let's deliberately rotate every player in as GM." We wanted everyone to get a shot behind the screen, learn what it's like, and give us all insight into strengths and weaknesses, so whenever one adventure finished up, we handed off to the next person. Even the ones that really sucked at GMing had something specific they did great that we learned from - dialogue, pacing, whatever. The campaign conceit was just that we were all pirates and were roving around on random adventures, there was no huge metaplot. We never had any problems with canon conflict or whatnot as a result, and everyone got some GM trigger time. It also made those who seldom GMed appreciate the GM more.