Gate fees are usually, not always, but usually tied to the owner of the ball park. If you want to hold a tournament at a certain ball park, then you have to deal with their gate fees.
About the only way to handle this differently is to include the gate fee in the team registration fee. So, 12 girls per team, a minimum of 2 guests per girl = 24 guests. $3 per day per guest = $72 per day x 2 days = $144 per team for a 2 day weekend added to the entrance fee.
As a TD, this is an option worth considering IF you can get the ball park to go along with this. Of course, the admission fee would be negotiable.