All of the following have minivans - all are reputable companies:

Bullseye - https://www.bullseyecarrental.com - Consistently gets excellent reviews. You can't go wrong renting from this company.

Avis - http://www.avisstkitts.com - typical AVIS cars and service.

Thrifty (aka TDC) - https://tdcgroupltd.com/thrifty.asp - locally based company - been in business for 30+ years.

Express - https://xpressautorental.com - smaller independent company.