I'm not to good at modding the AI files. I just look for the resupply facility and delete it? This must be done for each race I guess

If you don't make the value higher, tried lower but not equal, on the shipyard than the standard facility the AI will pick the standard facility at start.
You could add the Spaceport ability also and get 3 yards at start and that might work too but that doesn't seem as logical, I can see the yard and resupply being done by the same facility.
Do you think having 2 yards on a planet is worth it? I was hoping to get 7-10 yards and create a real important planet. Doesn't seem possible though.