[RPG] Should I change the entire campaign to please one player

This always seems to be the answer, but...

Talk to the player first.

I'm assuming you have some means of contacting your players outside your normal game time, if only to set up game or let each other know of cancellations or emergencies. Send your player a message, something along the lines of "Hey, I've noticed that you seem dissatisfied at game lately. Is there something going on you're not happy with? I want to make sure our game is fun for all of us, so please let me know if you have any concerns."

See how he responds to that. If he responds with a list of concerns, use those as a starting point. If they're things you can address, try to do so. If you think his problems are irreconcilable with your game and/or the other players, then say that, politely, and suggest that he might want to look for a different game to join.

If his response is neutral or brushes you off (such as "nothing's wrong, see you next game"), then you can let it go for a session or two. See how he behaves, and whether he raises the issue himself.

Ask another player to initiate communication

If you're not comfortable approaching the problem player directly (or don't have the means to do so), you can speak again with the person who told you this player wants to leave. It sounds like the go-between is friendly with him, so you can ask the go-between to, next time the player brings up the issue of wanting to leave the campaign, tell him to talk to you about it.

Don't use the go-between to actually convey messages like "I heard you want to leave, what did I do wrong?". That kind of thing usually gets lost in communication, and it puts the second player in an awkward spot. Just ask him to pass on that you're open to hearing your players' concerns and that the player is welcome to talk to you if he has a problem.

Don't jump the gun

Either way, don't rely on hearsay to drop a character and his player from the party. Don't allow the other players to sacrifice this guy's character unless you have his explicit buy-in (or if it comes up naturally in-game and the player himself is all for it). Don't assume that he meant what he said about wanting to drop, either - I've had players complain about my game in moments of frustration, but when I ask them if there's something I can do better, they reassure me they're having fun and were just briefly frustrated.

TL;DR: Communication is your friend!

Talk to the player. Follow his lead, and don't make assumptions based on what other people are telling you. If you handle this issue with grace and good will, then it's highly unlikely the other players will see a reason to stop playing a game they enjoy just because their friend did.

Your first question is about half a GM problem, and half a player/PC problem. I've been on both sides of this issue: GMing for a character who had little reason to participate in the story with the other PCs, and playing a character who had no reason to participate in the story and every reason to run wildly in the other direction. In both situations, the solution has two parts:

The GM finds ways to include the PC in the plot.

It sounds like your group is already doing this, but for posterity: this means that the GM must look for ways to actively involve the PC in the story, by using their background hooks, talking to the player about what the character might find interesting, and otherwise looking for ways to help the character find motivation within the story to participate in the story.

You do need to be careful not to change the story or the game's focus so much that the other players begin to feel excluded or ignored, but this is a matter of understanding your group, finding a balance, and getting buy-in from the player of the problem PC. Which brings me to part 2 of the solution:

The player finds ways to include their character in the plot.

This is the much harder part of the solution: the player must meet the GM halfway, otherwise the game becomes "The Problem PC Show!" and no one else has fun. This may mean the player has to bend or tweak the character in some way - not enough to compromise the core of the character, but enough to keep them with the group when otherwise they wouldn't stay.

This is, admittedly, difficult to do. Some people are so attached to their characters that they're unwilling to compromise; or they simply can't see a way to bend the character on an issue without breaking them completely. However, it's absolutely required in order to solve this problem.

Why player buy-in makes a difference:

When I played a character who had no reason to participate in the story, I looked hard for ways to make her want to be there. But all logic dictated that she run far away, find a hole, and pull it in after herself, so any other choices felt wrong to me. This showed in my roleplaying, and ultimately caused much frustration for our whole group as session after session became centered around getting her involved when she didn't "want" to be.

I put "want" in quotes there for a reason. Players with especially strong "my guy" syndrome (which I know I'm prone to) will insist that they're "just playing their character" and that "the character can't be changed". But when I GMed for a character who had no reason to be there, his player was willing to meet me halfway, and the result was a fun campaign for everyone where that character even made a large part of the highlight reel.

The reason it worked was because the player was willing to say, "he has no reason to come along, but does anyway, because that's how group-based RPGs work." We hand-waved it a bit as "he has nowhere else to go and nothing better to do", but really that character should have been as long-gone as mine wanted to be. But because the player was willing to take the meta option and bend his character enough to say "screw it, he's participating" without looking for a story reason, it worked. It kept the game from focusing too much on that character, but meant he was still there when story developments happened that he was interested in, thus giving him the time he needed to organically grow interested in the plot.

When the player isn't interested in the scenario

This part is a little trickier. If the player doesn't buy Dresden's world, including all the magic elements, what's he doing playing a Dresden Files game anyway? You and your co-GM need to talk to this guy privately, out of game, and ask him why he's playing. If he just wants to hang out with your group and doesn't care much about the game, then you need to address that. Maybe give him a character with a minor support role, so that he doesn't need to participate much in the game and can just hang out; maybe say that if he just wants to hang out, the game isn't the time for it and you'll find other group activities he can participate in. It's up to you and your group to decide what's best here.

If he insists that he wants to play the game, then you need to find out why he's actively sabotaging it. Tell him that his actions suggest he doesn't want to play, and in fact are making it harder to play. It's possible you simply have an attention hog on your hands, in which case you should deal with him appropriately. (I'd suggest going through the problem-players tag, as there are a number of questions and answers you may find relevant depending on your exact situation.)

TL;DR: The GM and the player need to meet halfway on adapting the character and the world. But if the player isn't buying the game's scenario in the first place, then that must be addressed first.