In Pegs & Jokers must I go past home in order to use a card I'm holding?
Yes, you need to move past your home spot.

I've found an explanation and detailing of the rules here. This website states:


  You must always use the full value of the card played. For example when playing a 6 you must move a peg forward 6 holes, no less. If you play a 6 when you have a peg on your in-spot and all your other pegs in the start area, you must move your peg on along the main track, since there is not room in the home track for a move of 6.