Most TV shows usually have several storylines with the main character's family.

On SATC, I recall one episode where Carrie mentioned that her father had left her when she was young. That's it.
Did the viewers know anything about Carrie's mom, or if Carrie had siblings?

When Carrie left for Paris, I guess she didnt have a big deal to worry about to tell her family. The writers made it seem that Samantha, Charlotte and Miranda were the equivalent to her family.

I know Miranda's mom died (based on a good episode, where the girls go to the funeral in Philadelphia) and her sister was named Betsy. Not much else.

Charlotte had a brother. He appeared on one episode (in one of the earlier seasons) as wanting to getting a divorce. He slept with Samantha, which made Charlotte upset. It is my assumption Charlotte came from a well-off family.

I don't think they ever introduced anything about Samantha's family.

They showed more of Steve's mom than they did with any of the four main character's family.

Did the writers feel that having a storylines that involved Carrie's family in someway would make the show too much like ordinary sitcoms?

I agree, we met Steve's mom, and even saw Aidan's parents once, but I find it hard to believe in 6 years, that Carrie's mom never came to visit her or vice versa.

I also find it shocking we never met Charlotte's family at either wedding (even tho we met Bunny, never Charlotte's side), and same with Miranda.

Oh well, small complaints but still you'd have figured there'd been some mention of them in 94 episodes

If the character had any living family, I am certain that they would have mentioned it. Maybe her parents were already dead when the show began. Perhaps she didnt have any siblings. Who's to say? But personally, I like the way the show centered aroung the lives of the women. If there was some one significant in their life, they showed that person. I suppose that for Carrie her friends were her family.