My mom's friend had two children before she met her boyfriend. He knew getting into a relationship with her, the kids were part of the package. He was always kind to them and treated them like his own. They were engaged to get married and she said she wants him to adopt them. He refused. They ended up in a 3 month long fight over it, called off the wedding, and separated for almost a year. They ended up getting back together but agreed not to get married until the kids were grown. His reasoning was that he didn't want to be fully responsible financially, medically, or morally for someone else's kids (another man) especially not when they are coming and going out the kids' lives.
Being with someone who has kids with another person can't be easy.