2009 Mazda 3 i-stop battery issue
 

Hello!
After visiting 2 electricians I came to this forum to see if anybody has/had the same issue as me.
Basically, the i-stop battery from my Mazda 3 is not charging (as the electrician I went said) due to a relay that does not get current from the ECU, however the MAIN battery is getting charged, so the relay does not do the "switching" correctly between the two batteries. The relay is fine, the batteries are fine, the alternator is also fine he said. I'm not sure if I understood it completely correctly, but that's what the electrician told me. Also, the voltage is dropping when I rotate the wheel when the car is on idle and I can barely see that the headlights intensity dims a little when turning when in idle. I even replaced the i-stop battery and the i-stop system stopped working after replacing (no error lights in the dashboard, will see on the OBD when it arrives). The i-stop was functioning before replacing the i-stop battery.
Can someone explain me what the real problem is and if is there any fix for this? Many many thanks!
The car is a 2009 Mazda 3 2.0 MZR DISI.

Good day.
How did you resolve the issue of i-stop battery not charging?