The Mounter would be a tool to help players mount (board or embark) living entities into vehicles.

A player right-clicks a living entity, e.g. a cow, with the mounter and right-clicks a suitable vehicle, e.g. a stock car. The entity is "pulled" into the vehicle in the sitting animation if available. This would replace the current mechanism which is by pushing the vehicle to overlap its hitbox with the entity's.

This idea is based on CustomNPCs' mounter which allows you spawn any living entity mounted on any vehicle.

I've thought about this too honestly.
One option that's available now would be to use a lead to bring them close and the railcraft ender rail to load them onto it.

there are some crossover tracks inside railcraft when you have railcraft and traincraft installed.
one is to "teleport" nearby entitys into the ... (cart with cow face on it) and another one to push them out of said cart