I have a lot of experience with players that act that way. I've had a player like that, at one time or another, so often that it sounds like you're describing my old games.
The one thing I will mention is that this is obviously something out of character related. She is frustrated, annoyed, angry, depressed, or some other emotion about something. And she's taking it out on the game. Since you only have four people and one of them has to be a DM, it's a hard situation to deal with.
This gets a bit into interpersonal skills and might not really be the best place to talk about this, but since you seem to be having a problem, here's what I can offer.
She doesn't want to play the game
It's very obvious from just the first two instances you posted that the player genuinely doesn't want to play the game. Playing a game is about getting into character and rolling with the punches. No plan will be perfect, your character won't know everything, and you're going to get into situations that you are not prepared for. Dealing with all of that is what makes the game fun. It's clear that she just wants to auto-pilot and coast through every scene. And you throwing wrenches into the plans is causing her to get aggravated. This is because she doesn't really want to 'play'.
She doesn't know what it means to roleplay
Maybe she's new to role playing completely, which is an option. If that's the case, she's having a large disconnect with what she 'thinks' she knows and what she actually knows. There is something to be said for a character actually having knowledge of a situation. But then, there's the world-building aspect. There are certain things that the DM will decide that the player has no control over. In fact, this should usually happen. And a player can discuss with a DM about the things they do and don't know or how they should and shouldn't act. But it should never be a case of 'I would never do X' when it's clearly against her character.
She doesn't want to play your particular quest line
I don't know your party dynamic, but it seems like she's poking holes in your game without reason. There is ample place for a party to get involved and have fun doing something in the scenario you've set you. However, she's actively making a character-breaking decision to not go along with the party. The group around the table should NEVER have to discuss for hours about going one place or another. This is a side affect of trying to pull a stubborn mule. The mule doesn't want to go and is going to make everyone else miserable as they try to drag it somewhere it doesn't want to go. And that's what she's being, a stubborn mule. It seems she doesn't want to play your particular side quest, for whatever reason. Maybe she liked the other DM better? Maybe she has something against you? I really can't say, as I don't know your friends.
The Solution
Since you have such a small group and you guys seem to be in the middle of a campaign that someone else is technically running, your options are limited. I would tell you to just let her know that her actions are pretty destructive to everyone's fun and inform her that she's not welcome if she's going to be a petulant child (use better words then that). But, you'd be down a player in the middle of a campaign, and that could hurt your friendship and game.
My suggestion would be to sit down with her, one on one, and talk to her about what's bugging her about the game. She might go over the little details and reiterate what she's said in game, but try to push past that and get to the root of the problem. See what she's really upset about. Maybe home troubles? Maybe someone at the game is frustrating her? Try to figure out possible ways you can tailor the game more to what she's feeling. Maybe she's sick of playing the previous type of character or it's not what she was hoping for. That happens. Try to work with her to either play something different or focus the game more on what she could like doing (keeping in mind the other players interests as well).
One thing I wouldn't suggest is an intervention. Those end badly, simply because the player will feel everyone is ganging up on her and alienating her from the group. Try to keep it one on one with her and let her know that you're just trying to help her have a good time.
This sounds like player behavior
I'm usually the one to point out way to address an issue in game. Not this time. I don't think this is a play style thing. From your description it sounds like this guy is having a little too much fun getting a rise out of you.
The player's behavior is really a bit out of line. Constantly hitting on every NPC of course requires you to play their part. (And that's been more fun for him than for you.) He may be hitting on you, or just trying to provoke a response. Either way it's not OK. You've made it clear this is no fun for you, and he hasn't changed his behavior.
The Details
Hitting on the celibate priestess, well that's just a little "challenge." There's no problem with someone wanting an in-game girlfriend who's a powerful figure like a chief priestess or a powerful adversary. Abandoning his party and getting a PC killed, that's not cool, and the other party members won't be real keen on that.
But that's all in-game stuff. And what you describe goes a little beyond that.
Respect
It all comes down to respect. If a player is disrespecting you (or anyone at your table) then that is cause to eject him from your game.
Fantasy vs. Realism
Since answering, the question has been updated to specify that "realistic relationships of all kind are OK." But while you might be able to encourage a person to be more sensitive and patient in a their courting efforts, it probably isn't realistic to expect them to fantasize what you want them to.
If the player would like to role-play like a chick magnet from a Heavy Metal comic, it's not likely you'll convince him it would be more fun if in-game courtship were more like "real life."
Going forward
If you're not ready to disinvite him yet, let the table know that the game is going Rated PG. (I'm guessing most of your players will be happy with this.) Don't role-play the romance with the fellow. You could allow the dice decide whether he impresses a female, and describe her reaction matter-of-factly, all in the third person, as boring as possible.
If he doesn't simmer down, you need to ask yourself if you are comfortable with the behavior. If you aren't, then he's got to go.
Best Answer
If you are not in a relationship, this is not an RPG issue, it's a relationship issue.
Being in a relationship in-character is a heavy emotional romantic thing for many people. It seems that this woman is one of them... and she's using the IC relationship between your characters to be halfway in, halfway out. Almost-relationships of all sorts are really very tempting for people who know that they can't be together with the object of their affections (because it's a terrible idea, or the other person won't agree, or parental disapproval or whatever) and they are emotionally super-complicated and they're basically a relationship in disguise. You're not enjoying the in-between state, and she's clinging to it. You need to work this out one way or the other. The process is likely to be messy. I suggest you get some advice from the Interpersonal Skills stack first, as they're the specialists at this sort of thing. Aside from that piece of useful clue, though, your underlying issue here is out-of-scope for the RPG stack.
If you are in a relationship, take it offline.
You are in an actual relationship with a woman who apparently really likes roleplaying as a character who's in a relationship with a character you are playing. That doesn't have to be bad. It can be fun. The core RPG problem that you've described that it's distracting from play at the table. That doesn't have to be an issue, though - you're in a relationship already. Presumably you're interacting romantically at times where you're not gaming, and "your characters roleplay having a relationship" is the sort of thing that doesn't generally require DM adjudication.
So talk with her about it, presenting the issue as one of not wanting to be rude. Suggest that you take it mostly offline. When you're around the table, it's time to game in a way that everyone can be involved in. You can indulge in "couples roleplay" in your own time when no one else is waiting on you.
If it's not so much a matter of "This is interfering with the game" and more a "I don't enjoy this activity" then the issue is that you're in a relationship with someone who really enjoys a couples activity that you're not so into. At that point, it's a question for the Interpersonal Skills stack.
Alternately/Additionally, consider getting involved in some sort of LARPing scene, where two people pausing for in-character romantic interludes doesn't interfere with other ongoing stories in nearly the same way.