You do not have to friend anyone you don't want to. That includes your parents, your boss, your coworkers, your ex-boyfriend, your previously unknown illegitimate half sister who just introduced herself, and that person who bullied you in elementary school.
However, if you don't want your mother/kids/boss/sister-in-law seeing what you post, then don't friend them in the first place. Don't friend them and then expect them not to read or react to what you post.
Don't be insulted if someone declines your friend offer. Some people like to keep Facebook only for their peer group, or only for close family and friends, while others like to friend everyone they possibly can.
In the same vein, being defriended isn't generally a deadly insult. People defriend when they are paring down their networks to people they have regular contact with. People can also defriend when it's a simple mismatch between posting styles and usage, or when there is little activity on someone's account. It doesn't necessarily mean someone doesn't want to be friends with you in real life.
You can't control the interaction of your friend list with each other. If you friend two people independently, then they are free to friend each other, or start a real life acquaintenceship.
At the same time, you are free to defriend someone who is acting inappropriately towards your friend list (like sequentially asking all your female friends out, or trying to sell them a pyramid scheme).
Facebook etiquette and friending/defriending policies apply across generations. If you are in the older generation, accept that your younger relatives may not be keen on having you as a friend and don't push it. If they do friend you, then keep a reasonably low profile while you figure out what their style is.
If you're in the younger generation, realize that your older relatives are not likely to be as amused by pictures and postings involving drunken or debauched behaviour as your friends are. If what you post is worrying enough, then yes, they may legitimately talk to your parents about it.
Finally, remember that a Facebook friendship really doesn't imply much about a real life friendship. People can be fantastic friends without Facebook contact, or totally indifferent in spite of reading each other's status updates on a daily basis.