The central conceit of the first few seasons is that Buffy is leading a double life. People in "the real world" don't recognize Sunnydale as the supernatural hot spot that it is, and meanwhile Buffy's pressured with normal family-and-school expectations in addition to her slaying duties. The implicit assumption is the Buffy's mom wouldn't believe her, or would freak out and try to stop Buffy from protecting Sunnydale, or would otherwise cause a whole bunch of trouble if she ever found out what was going on.
Kendra is presented as a contrast to Buffy - somebody whose entire life is devoted to being the Slayer. This is portrayed as what's "expected" of slayers, particularly by the Watcher Council - and we can see that Kendra is kind of "all slayer, no teenager." Kendra's parents knowing about vampires and slayage et al, and training her and giving her up, is an expression of how Kendra's total devotion to being the Slayer has wiped away any connection she had to a "normal" life.
In later seasons, Joyce's role in the series changes rather drastically. The truth about Buffy and Sunnydale gradually become public knowledge, and we certainly see that Joyce can know about Buffy. Of course, this comes with tensions and complications as well.