That's a tough question.
Technically, a league is its own legal entity and as such, as league can choose to go to a different center. The league votes on the league officers.
For certified leagues in USBC, there are two concepts of leagues. The normal type, where a league has its own full set of officers and what is called a MANAGED league, where the center does the league processing, secretary work and essentially runs the league. With a Managed league, there is a requirement that a president be voted and that the president not be a family member or employee/owner of the center. This is to protect the bonding for the monies.
A center certainly has the rights to not let a person enter their establishment. This would make things difficult for the secretary to do their work, but not impossible. The center can certainly drum up support from the league board to fire the secretary.
If this is a USBC certified league, I would suggest going to BOWL.COM and contact the national rules committee for clarification and options.
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