2002 Ford Taurus when lights turn on car studders and will

I thought it might be a voltage regulator problem but after changing the alternator and having no effect on the problem I am stuck! Car ran perfect over to a tigers game and as we left the parking lot this all started! So with no lights on it runs perfect, once even the running lights are turned on the car begins to have a stud-er you can hear and feel while doing 80 on the freeway and the lights in side the car flash when it does this. Could be as simple as a bad battery wire? I checked that and it is always perfect so no problem there I am thinking maybe a short someplace? Help Please!