The unequivocal answer is yes. Over the years fathers are becoming more active in their child's life. Studies have shown that when a child has a father in their lives they grow up more secure emotionally, have better social skills and have stronger outside relationships. Being active in a child's life is just part of it. Studies have shown that when there is an active father they develop confidence and less likely to get into trouble both at home and out in the community. Drug usage tends to decrease as well as the use of alcohol. It is even been proven that children with fathers involvement increases their childrens IQ and behavior.
Fathers have such a critical role in their daughter's life. When she is learning how a man should treat her she is going to be looking to her dad as her first male role model. Depending on her relationship with her father she is learning how to be treated by other men. Girls should feel like a princess and learn from the way their daddy treats her.
Both boys and girls just want to spend time with their dads. They don't expect dads to take them somewhere or to buy them something, they just want to spend time with him.
Provider and Protector
Fathers play such a key part in the child's life but many times that relationship isn't nurturing. No matter if the relationship is traditional dads need to make every effort to support their children both financially and emotionally. Dads need to demonstrate their role both as a provider and the protector.
There is no right or wrong formula when it comes to being a father however the Bible teaches us that dads hold a unique ability to bless their children.
Fathers need to strive to bless their children everyday. Dads who don't try to be Christ like are missing the most important influence time in her life.
Fathers and sons
Fathering a son is a little different than fathering a daughter. As the father of a son its his job to teach them how to treat girls. Children mimic what they see and if they see their fathers treating both moms and daughters with respect and love that is how he will treat them. Girls should be treated like ladies and goes above and beyond to make them feel special then that is how he is going to treat them. Start teaching your son's from day one how to treat his mom. Teach him at a very young age to open doors for them and pull out their chairs.
As critical as a father/daughters relationship is raising a son who respects women starting with how the father treats his mother. There is no one else he looks up to more than his father. Teach him that regardless of how the women/girl treats him that he should continue to treat her like a lady. The rest will fall into place.
When looking for a lifelong mate your daughter is going to have high expectations in how he treats her if the foundation is already there. The same is true with sons. If he is taught how to treat a girl from a very young age it will be second nature to him for the rest of his life.
So the final answer is yes fathers play a critical part in his children's lives.