Great advice!
When you marry someone, you are marrying a family.
When I was dating my now wife, she had two grown boys, 19 and 20. The 19 year old was still living with her. I knew from the start that it was absolutely necessary to develop good relations with her boys.
I had a daughter who was a high school senior. She was a single mother living with her mother. She and my granddaughter spent a lot of time with me. She was comfortable with this woman.
We have been together for 30 years. We have both been accepted as members of each other's families.
I was taught by experience. After my mom was killed in a traffic accident my dad remarried. In this case, it wasn't that I didn't like my step-mom, she didn't like me. She was always gratuitously insulting me and making it clear that I was a failure and a disappointment.
At one point, dad arranged for us to visit a family therapist. When he explained that we had to resolve the issue as a family, step-mom insisted that i was the entire problem and she didn't need to do anything. That ended our attempt at therapy.
Curiously, when I grew up and left home, we grew closer. We became so close that when she was dying from cancer, she would confide her deep fears and sorrows over the prospect of death. I did my best to comfort her. Now, I miss her even though she has been gone for over 30 years.
Not only is it important that your children like your date, he or she must like your children as well.