My PC case has 3 fans, but my mother can only have 2?
Is there an adapter that lets you connect the case fan connector at one extreme cases gives you a 2 connectors on the other end? So basically 1 or 2 Chassis chassis adapter?
No. The only supply connections a certain amount of power. While you could run two fans off it, which could overheat at worst and at best fans would not be full capacity. Buy a different motherboard, leaving a fan off, or get fancy with a soldering iron.