All you should be doing is making her an offer for 1/2 of any increase in value of the home over the purchase price, together with any down payment she provided towards the house. If she says no, that she is entitled to half of the entire equity of the house, suggest that she speak to a lawyer because you are not willing to agree to unjustly enriching her.
Put your offer to buy her out at the current Fair Market Value of the house, minus purchase price and leave it at that. She will lose horribly in court should it actually make it that far. Chances are she is just trying to bully you into giving her extra coin that she doesn't deserve and isn't entitled to. So call her bluff and make her talk to a lawyer who will hopefully set her straight about what she is actually entitled to.
Should she actually take you to court, you provide them with your written offer to her to buy her out at FMV - purchase price + any down payment she provided, and ask for costs of the action, because she is wasting the courts time.
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