I get that stories need set up but with a manga the first chapter has to grab you and ones like this that load way too much into too few pages really just need to get to the point. You can circle back later to further explain things.
Royals are usually hands-off with their children as long as they don't do something incredibly stupid like say trying to rape the daughter of the countries most powerful general. Also, you can't blame a parent for their child's mental illness.
My interpretation is that the (rookie) god who did the summoning was trying to combat the corruption of the stone, meaning it already existed and was in use by the time the MC was summoned. My theory is it's the magic stone of the demon lord.