After that explanation, I can't say I condone your decision to wilfully violate the rules, especially since you're an umpire. Take the following as an example...
In one of the leagues where I call ball, one of the umpires (I'll call her "Julie") in our crew plays for one of the co-ed teams. Turns out one of her teammates is known for bringing doctored bats (they look like Freak 98s) to the game (see
this post - same guy). "Julie" has heard these reports as well, and decided to see for herself if the bat was really doctored. She takes her own Freak 98 and compares his with hers. Sure enough, inconsistencies are found.
At this point, Julie had a decision to make. It is known throughout the area that she calls for our group, and she has a reputation to uphold. On the other hand, she wanted to play, as she loves the game.
In the end, Julie told her team captain, "either the bats go, or I go," and she stuck to her guns.
While I can't tell you what to do, tmielke, it would be wise to think about what it means to do what you did: wilfully violate a rule for the sake of winning. It would also be wise to think about the fact that this is a 12U team, and doing what you did accomplished 4 things:
1 - The kids now believe you must win at all costs, even if it means violating rules, or
2 - Your decision was the correct one, and the kids now think this is the rule, and
3 - If the illegal sub got injured, you're now opened up to the possibility that a slick enough lawyer could argue that as an umpire, you should've known better, and you're responsible for her injuries.
4 - You've possibly now gained an ill reputation among other umpires in the area, some of which you may or may not call with. However, you'll probably face them again, and you've lost credibility with them.
Just food for thought, and that's all I'll say, coach.