Can I change a tub drain from left to right? Is there a lot involved

Can I change a tub drain?

Well, you can't just pull one tub out and put another one in. All depends on the plumbing, both drainage and water supply piping. At a minimum it would involve cutting in to both the floor and the walls to reroute piping, if, if it can be done at all. So, yes there is a lot involved

It is a major pain in the neck for most home owners. Get 3 bids first to see what it would cost. Pick their brains to see if you can figure if you can do what they plan.