It's hard to find someone to love you and accept your kids to your past relationship. Them, accepting your kids may be easy but sincerely loving them is a different story.
When you're a single mom and you finally found the guy that is willing to love you is a fortunate thing but when you find that guy that loves your child too is a blessing.
Not everyone can accept and truly love the child from the past relationship of their current spouse or partner. It takes a real man/woman, someone mature enough, to accept and love everything about their partner, including their children.
Some ended up being a bad stepmom/stepdad. They not only make the child's life miserable but also makes their loved-ones (parent of the child) miserable as well. Being a bad stepdad/stepmom is something that makes the parent feel like it's a living hell. Like they always have to choose between the lover and the child which they try so hard to let the other understand that it should not be the case. And worst is when the couple has their own child. If you're a bad stepdad/stepmom, you will always make it like a competition. You will always see what's wrong and which one is more or less than the other. Which is a very wrong thing to do. This time you are even making it hard for your child without even knowing. It will affect your child in the long run.
Being you as his/her father is as important as them being his/her half-sibling. Your child shares DNA from you and so does his/her other siblings. There's no point in making a point in which one gets what and/or which one should he more loved. You, your child, or the other child.
She loves you because you're her husband. She loves both her child because she's a mother, regardless of who the father is. She is and she will always be their mother. The same goes for men. He will and he will always be the father of his children regardless of who their mother is.
So why compare how she treats her children. Every child has their own needs and unique way of discipline because every child (every person, actually) has their own personality and characteristics. And every child has their unique experience and mistakes and/or circumstances. They should be acknowledged, understood, cared for, disciplined depending on the circumstances.
I have observed a lot of such situations where they are stressed on how to make the family more like a real family that doesn't have any divisions or any of that sort.
If you think you can never accept their child before your relationship, then don't go trying to build a family of your own with her disregarding her own child. She will never be happy and lives will be ruined.
PS: This isn't my current situation. I just read a post on Facebook about this and I felt bad for the girl and thought maybe I can make it a topic worth writing.
It is worth writing since not a lot of people actually want to discuss the matter publicly. It usually just remains behind closed doors for reputations and such