Without knowing the details of the negotiations and the pre-nup itself, it is hard to really comment meaningfully or take sides. Maybe you were a total B about it, or maybe just so business focused it made him uncomfortable. Or perhaps he is trying to get more from you than he deserves.
Mind you the 2 main things couples argue about are sex and money. Money should be simple.
In the US most states have mutual property laws, which means that all money and assets belong to both people. That means pre-nups are important, and are supported by the courts. In many other countries the process is far more complicated. In the UK, your partner, on being divorced, should be allowed to maintain the lifestyle they enjoyed at your expense, while in Australia financial resources are split up based on how much each person contributed, individual needs, and so on.
Anyway,
You have no financial responsibility to his daughter, even in a relationship, and should the relationship end, and you have given her shares, you may not even be allowed to contact her, but she still owns part of your company
You have already been pressured to financially contribute to his daughter, which maybe you shouldn't do, and it should be his responsibility, while you would be better off with one offs, like phones, holidays etc
Pre-nups should be simple
Everything you own before the relationship is yours, everything they own before the relationship is there's
Anything you do with your business is yours, and their own income or business is there's
There is no responsibility for children or family of the other person unless adoption occurs (which you might choose to do later)
Caveats include
Contributions to a business or work should be factored in, such as you working 12 hours a day 7 days a week on your business, while he helps you without pay, means he is owed something, or even if he maintains the home, cooks meals, while you work, then he is owed something
It changes if you and he have children together
But basically, if you can't settle the financials, then there will always be resentment. Doesn't even matter whose fault it is.