The OP’s feelings about the daughter are a red herring. In this specific dynamic, suppressed feelings about the relationship between the adults are nearly always transferred onto the step child.
My sense is that the OP’s partner has somehow engineered a ‘competitor’ dynamic: whereby the OP feels she is competing with his daughter for his attention. But if you boil it down, what this essentially means is that the OP’s DP isn’t investing enough in his relationship with her and OP feels left wanting. In short, as is so often the case, she has a DP problem.
When a single parent wants to start a relationship with someone childless, the onus really is on that parent to make sure that if the relationship goes ahead, everyone is able to get their emotional needs met - not just the parent and the child, but the new partner equally.
When you are a childless person, it is a massive ask to emotionally invest in a relationship with a child who isn’t yours. So often the perspective is all backwards. The new, childless partner is expected to be grateful to be afforded the privileged opportunity of having to come second best all the time to a child whom they do not really know very well at first. And, the cherry on the top is that they are also expected to regard it as a privilege to have to provide child care and carry out in loco parentis obligations without any thanks or credit.
But the reality is it’s not all that an attractive proposition for a young, single, child free woman with a whole future ahead of her. Women who embark on step-motherhood do so out of love for their partner primarily, and often quickly realise that it is all too easily taken for granted and used as emotional blackmail against them.
The situation the OP describes is so, so very common that it simply cannot be the case that there are thousands of evil, selfish step-mothers out there who all hate and resent their partner’s children.
More likely odds are that there are thousands or women who feel they have sacrificed their child free lives and their future potential relationships, to go all-in with a man with children, and are getting very little consideration in return.