Is there any relationship between ice time for a player and the financial contribution of the player’s family towards the team?
Absolutely not! This should never be allowed! There is no doubt that it has happened. Unless your team has a special rule that states otherwise, each family pays the same amount to be a part of a team. If there is a known and proven correlation between player’s ice time and parental contribution to the team, then it needs to be dealt with immediately at an executive or administrative level.