In training and unwilling to falsify logs to help my trainer make $. What to do?

Stay with the company, tough it out. Do with your logs what you see fit. As long as it's legal, you are fine. Let your trainer complain. When your trainer calms down, explain it's your CDL, not theirs.

Edit: Just noticed how old the original post is. Still, feedback is valid for anyone who comes across it.

 

It should have been logged yard work, if the customer yard was a private property where the public access was restricted.
Know the law, follow the law.
You are the only one responsible for filling a federal document:
Your log-book.

 

It depends on the company how exactly it is logged. Because different companies have those pre-typed entries for the e-log worded differently. Some it is on duty and then select whatever function is being performed.

 

It's not what you log, it's how you log.

 

This is where understanding the fine print about the rules concerning breaks may come in handy, in some places provided you are not behind the drivers seat any time spent off the drivers seat can be counted as non - driving time even thought technically your still working. So yes there is a fine line as to whether you have to actually be taking a proper break or as long as your simply not driving as to whether it can be counted as a break or not. Personally if your sitting in the passenger seat there is no reason why you can't count that as a break.

 

Per the reg's onduty time counts as part of your 30min break