Toyota Repair Problems? Ask a Mechanic for Answers ASAP
Thanks for posting,
Did the Toyota dealer give you any diagnostic trouble codes? It does sound like possibly an electrical issue causing a misfire. If you don't have any code information can you get it to an autozone or similar parts store to have them read the codes, they do this at no charge then please reply here and I can help some more with this.
Possibly a sticking fuel injector or a bad coil, unless there is lots of smoke from exhaust I doubt the headgaskets are the problem.