I believe the answer is:
A deck of cards (as Brent Hackers sort of points out in his answer and the comment from OP)
Captain, I am willing to bet,
That yar will never get,
The meaning of this riddle!
You bet on card games specifically the various forms of poker.
Many siblings live together,
Referring to the Jack Queen King I believe
Sister and brother equal in number,
There are 4 Queens and 4 Kings which I believe are the siblings
Many many pets but not a fiddle!
No Idea, maybe the number cards are the pets
Sometimes they're at war.
Refers to the card game war
And sometimes they swindle yar,
Sometimes people cheat in betting card games
But they truly amaze a kiddle!
A deck of cards is used in a lot of magic tricks that will amaze children (and adults alike)