Brenda,
before you replace the baby or the bath water........
these machines are not known for starter failure, it's possible but not probable.
with that said, might i suggest you have a look at a few common concerns before you proceed?
the few catastrophic failures of these machines can be traced back to a bike that has set for a long period of time and the needle and seat in one or more carburetors will get gunked up from old fuel and cause the float to stick and allow fuel to flood the carburetor until the point that it overflows and fills a cylinder with fuel and eventually seeping into the crankcase and causing what is commonly called a hydro lock and not allowing the pistons to move because there is too much fluid / gas mixed in with the oil or sitting on top of the piston.
so before you jump it or add to much power to the system and possibly causing bigger damage i would suggest a look at the fluid level in the oil sight glass and make sure it is not way over full.
if you find an over full issue, you will need carbs cleaned and new needles and seat gaskets.
and a oil and filter change.
if that is not a concern, i would proceed to the starter solenoid to check for corroded connections due to a poor location that mother Yamaha put it.
a dirty connection at the solenoid would still allow a good show of lights and a good battery would not overcome.
this solenoid is in the same place on your trike as it would be on the two wheeler and just as much of a pain in the a$$ to access.
remove the rear floorboard two bolts on the kickstand side/ left side of the trike and you will see a single allen bolt holding the half moon shaped chrome cover in place.
remove this cover to see and locate the solenoid and clean as needed.
not looking for a debate or a battle of text. just giving my $.02 for a .0$ price
Mike