You're not playing the same game
And when people in the same group try to play different games at the same time, there's a problem.
You did good by talking to your player - that's usually the first and also often the last step needed to resolve such problems. However, your player seems to be adamant that their style of roleplaying is the only way to play even if it's to the detriment of the other players' fun. That's a behavior you need to address.
First of all, you're playing Dungeons and Dragons 4th Edition, whose rules you can rely on in some cases to reduce the impact of individual incidents. For instance, you say:
the party is struggling to find tiny murloc village in the dense forest while he insist to stay at camp and roll the dice to "plaid her braids". And until it's 15+ he won't move forward (got it? they have to be on fleek), because Ivy (the princess) wouldn't do it as well.
We had a similar problem in one of our games - a player who wanted to avoid combat by calling skill checks to negotiate, bluff and then escape. That hurt the tension and was a bother to everyone in the group who wanted to fight. However, the rules state that the problem player has no business calling the rolls - that's your job as the GM. That's one of the very first rules in the book:
All these actions depend on very basic, simple rules. Decide what you want your character to do and tell the Dungeon Master. The DM tells you to make a check and figures out your chance of success (a target number for the check).
As the GM, it's up to you to decide whether something needs a check or not. So, the next time the problem player tries to invoke rolls to kill time doing something menial, you can simply declare these actions to succeed without a roll and get on with whatever you were doing. Do not feed the problem player with more table time or attention. If the player protests, keep your calm and say
"I'm sorry, but these are the rules and I agree with them."
Be honest and open about the kind of game you want
While applying the rules right will make some situations less sticky, the core issue remains: you're playing DnD 4e as heroic fantasy, the problem player isn't. You need to be open to the players as a group what the game is like and what you expect of the characters. Making certain requirements of one's player characters is a common way to avoid some basic problems in RPGs: eg. many groups rule out Evil characters or ones disinterested in adventuring, and the very rules of 4e rule out "average" characters in favor of clearly superior heroes.
When doing this, you may receive criticism from the problem player: some players have very strong opinions about certain playstyles being somehow wrong or a worse kind of roleplaying (eg. the heroic fantasy questing style that's common with DnD, especially in 4e). This is not true, but it's something you might have to address. If the problem player complains, do your best to remain calm and explain that you are having fun playing in your way and aren't changing the entire game to conform to their character.
If they persist, kick them out
Sadly, sometimes even our closest friends make for awful RPG company. If the problem player persists in their resistance, there's no point in you putting more energy in trying to minimize the damage they're doing to your game. Tell them they're no longer welcome to the table because they want to play a different game than the rest of you.
However, you can soften the blow using the following:
Run (or ask the problem player to run) something else
Dungeon and Dragons 4e is tailored for a very specific style of gameplay and doesn't work very well when other styles (like simulationism or acting) are shoehorned in. Playing something else between your 4e sessions can help your problem player better grasp the idea that there are different games that are well-suited for different kinds of things, and let them engage in playstyles they find rewarding. Try introducing them to games like Apocalypse World, Fate or 7th Sea and see how they respond to these, or something simpler like a game of Roll for Shoes (full rules in tag wiki!).