Stuttering starting

Hi,

This sounds more like the fuel pump. The alternator has nothing to do with starting the vehicle. It only supplies needed voltage after the engine is started. The starter also would not make sense just because it actually starts. The starter just spins the engine and once it starts the starter is finished. So if the issue is sputter once the engine is started, then this points to an engine running issue. Sputtering is normally always a fuel issue so when you say it starts after you turned the key again, this is because when you first turn the key the fuel pump pressurizes the system. When the pump begins to fail it doesn't send enough fuel so turning the key off and back on causes it to do it again and this time it supplies enough pressure. I would replace the pump and go from there based on this info. However, here is a test on how to check the pump:

https://www.2carpros.com/articles/how-to-check-fuel-system-pressure-and-regulator

They are going to try and duplicate your concern and then check for codes. That machine does not test the fuel pump. You need to actually hook up the fuel pump. What I would do is drive the vehicle so that you know how to make it do it and then go take one of the dealership advisers or techs for a drive and you show them what it does. Unfortunately all to often they don't drive it enough or like you need to in order to get it to act up so they just tell you nothing is wrong.