Potentially, commenting on appearance is sexual harassment. It's a bit of a 'nuclear' claim though - you couldn't realistically expect to stay there after you'd made that type of allegation. I presume that in a family company there's no sympathetic HR person to have a quiet word with?
The nepotism bit is difficult. Yes, legally, he can favour anyone he likes over anyone else. What he cannot do is favour or disadvantage them for legally protected reasons (age, race, sex, religion, disability, sexual orientation). That means that I do not see a claim just because he treated his daughter better. Occassionally, if the treatment is really bad, you could claim 'constructive dismissal', but that's really about them being nasty to you, not a comparison to extra-favourable treatment to one other person.
BUT it can be sex discrimination not to allow part time working without good reason. The fact that he was willing to agree it for his daugther might show why there was not a good business reason to turn it down.
The caveat to that is that employers are allowed to take into account the make up of their team when making decisions. The easiest example is if you think of a 2 person team where the phones have to be covered from 8am. If the first woman makes a request to start work at 9:30, that might be fine. If, later on, the second woman also asks, it might have to be turned down because it would leave no-one to cover. Thus, if the team can only accomdate one part time person, that might be a legitimate business reason why she got permission - i.e. that she just happened to get in first. Unlikely, but possible, depending on the type of work you do.