This is all a bit messy.
They didn't trawl facebook just to find dirt. People do it all the time now as part of recruitment process - it adds a whole new angle to your knowledge of a person. People should be SOOOOO careful about these sites: it is a gift from heaven to mgmt.
Whatever it was you put there did genuinely upset somebody, regardless of your intent. It would have been better if on the day oyu joined this had all bveen brought out into the open wiht HR and so cleared the air, but of course you were upset, so I can see why it didn't happen.
so. He has grounds for being upset. You have grounds for being upset. Adn there's a girl floating around who may/may not be good at her job but is the bosses daughter, so you perceive that she is getting preferential treatment. Now that might be the case but whether it is or not doesn't matter, because it isn't a situation that you can change.
I think you have two choices here:
(1) Go to HR and explain that the department as a whole is not gelling well and you think it is affecting your work; can they advise? I personally think managment should get involved here because the department has got lost in terms of everyones' perceptions of what is and isn't fair. It won't get ant better by itself
(2) You could find another job.
going down the first route might resolve this and help everyone work better together, and if it doesn't get resolved you need to get out of there because the air is toxic as far as your own personal position is concerned. If you go down the first route then HR might suggest you leavign the department anyway as being a good course of action, in which case they may try to find you somethign else or you may be able to negotiate a compromise agreement (and negotiate time off to look for other work, which is always better than leaving without another job)
In terms of whether the organisation has acted unreasonably towards you, then I can see why you are upset but personally I do nto see you as having a particularly strong case for claiming constructive dismissal or suchlike, and if you have been there for less than a year your rights are limited. More importantly than this, you are obv. quite upset by all of this and moving on rather than embroiling yourself in legal action will be the fastest way of getting yourself to a better place, mentally. I don't think you'd enjoy the fight.
The third option of standing and fighting your ground and telling them they can't do this, they can't undermine you, etc, etc, won't (I think) help you here. The 'value' of them (your boss and this daughter) is probably more than your value to the company. Which is not to say that this is right or that it is your fault. But it won't change. You need to either get HR to step in and clear the air so you can all 'start gain' or you need to move on.
IMO, all of this. Not sure if HR peple will say the same....