Car shakes when turning right with the gas pedal pressed

Hello, accelerating while turning causing the car shake sounds more like an engine performance issue that is being stressed further when the power steering system is being used to assist steering turning. It's impossible to say without testing hands-on. There could be other issues here, but the most likely one is that there are basic engine performance issues that must be resolved. Use this link to find some shops near you that can help with your concern: www.repairpal.com/repair-shops