LL allows participation in other programs.
The only restriction is that an all-star player (one on the all star affidavit) cannot play elsewhere starting with the all-star teams first game through the team's elimination from the LL International Tournament.
The rule is on page T-4 in the 2004 LL Rule Book
"Participation in Other Programs
"A player may participate in other youth baseball programs prior to the first game involving that player's team. Once play begins for a tournament team, players named on that team's tournament affidavit may NOT participate in any other youth baseball program until that team is eliminated from tournament play."
Perhaps your league is misunderstanding when it kicks in. The restriction is only in the tournament rules section and thus applies only to the tournament (all-star) team.
This is covered in the LL FAQ at
http://www.littleleague.org/umpires/...echangefaq.asp