How to fix this one...
 

I'll start by saying that I take full responsibility for this mistake. It was hot and humid, I was in my 5th game and I lost my focus, allowing something to happen that obviously shouldn't have. And yes Cecil, trouble seems to have a way of finding me :o

Here's what happened as it unfolded. Bases loaded and I'm field ump in C. 4 straight pitches for balls and pitcher walks in a run. The runner who was on 1st comes to second. 2 more pitches are thrown to the new batter when the defensive coaches comes out and says "hey, hey, isn't that girl that's on second supposed to be out? Didn't he (meaning me) call her out a minute ago?" My partner at the plate meets with me and says, "didn't you call her out at first when she batted?" And honestly, I couldn't clearly remember. Looking back I believe I had a very routine out (both me and my partner had a recorded out on our indicators), but then I didn't look at first anymore. Apparently the base coach simply kept her there and "got away" with it.

My partner pointed at the runner on second and said "you were called out", and the runner smiled and went back to the bench. No arguments at all from the offensive. The run that was walked in was allowed to count, because we didn't see a way of returning a scored run after pitches were thrown. We finished the inning, talked about it and decided that I obviously blew it and that the team cheated and got away with it (at least for awhile). I don't like to throw the cheat word around, but this team continued in this game and in others to ask to put improper subs and improper courtesy runners in the game (all caught before being accepted). Each time there was a "my mistake" and we moved on.

So I blew it and I know that, but what would anyone have done? Any rules covering something such as this?

Yes, "umpire jeopardy". The illegitimate move by that runner or coach had to be corrected. Both should be restricted to the bench.

This is the crux of the issue:
"The run that was walked in was allowed to count, because we didn't see a way of returning a scored run after pitches were thrown."

I guess you were correct about after another pitch; but hopefully another solution exists.

Which rule would you cite in any sanction for restriction rather than an unsportsmanlike ejection in this case? Knowingly and intentionally cheating should never be treated that lightly, in my opinion. Make it hurt as much as you legitimately can to stop that nonsense.

We did discuss potential ejection, but since I couldn't definitively recall the called out, it would be easy for them to say they "didn't know". Was I loud and clear enough? I know I used proper mechanics but I was blank about the particulars. Their pattern for breaking the rules revealed itself as the weekend continued.

Only the "doubt" about the occurrence.