I believe most parents, even if they are happily married have different ideas on how to raise their children. My parents divorced when I was young and so they got to freely express their parenting styles without compromise to the other. My father remarried quickly and my step mother became the prime reinforcer.
My mom is a very permissive parent, I could do no wrong growing up and if by chance I did there was little punishment. I spent more time with her growing up and still do so I believe her parenting has rubbed off on how I treat others in life, I get upset at first when someone does something wrong but in the end I still am very affectionate. My boyfriend can get away with basically anything.
At my dad's house my step mom took an authoritarian approach to bringing up me and her two daughters, except for when we got in trouble then there was severe punishment. As we got older, she got busier and was less involved in our lives and what we did. My sister, Nicole started sneaking out and taking part in illegal activities. Rochelle retreated into her world of books.
I think parenting styles change as children grow up or as parents become busier. Nicole has always been more of a risk-taker than me or Rochelle. I'm not sure if this is a result of her mother becoming uninvolved in her life or because of the uninvolvement she was able to try more things she'd always wanted to. Rochelle has always been an introvert, and I feel like it was only natural for her to retreat into her book world when her mom became uninvolved in our lives.
In my opinion, no matter what is the style everyone is growing his children, they need both parents even if they are divorced. But sometimes moving from one to another parent's family could be very hard for the children and parents must be careful and have a good coordination! Children with divorced parents are really many, but they need a little additional attention!