Question: At what age should a parent stand aside from assisting their kid in their shots?

Answer: That's a curly one. Some tour players on both the LPGA and the PGA ask their caddies to check their alignment or assist with reading putts before a shot. It's perfectly legal. 

However, when a child of (say) 6 years is just starting out in the game it'd be perfectly normal to expect the parent to guide the child through their pre-shot set-up. However, the degree of assistance should change as the child grows, as technically speaking a caddie cannot "coach" a player during a competition round.

The Callaway Junior World Championships prohibits caddies after the 7-8 Years age divisions. As such, from the 9-10 age divisions a player at those championships is not allowed any assistance from their parents or coach during their round. it's somewhat a test of solely the players ability rather than of assistance of a caddie who perhaps is quite a skilled golfer in their own right. (Fortunately though, at least the 9-10 years at that championship are allowed to use a push-cart.) Other prominent junior tourneys such as the US Kids World Championships and The Optimists International do however, allow caddies at every age level.

It's an interesting situation, as Tour players are allowed caddies, and many of those caddies are elite golfers in their own right too. The underlying conundrum though is to decide as a parent when it's appropriate to let your child "call the shots" independently of their caddie. If they're making their own decisions, then they may learn quicker, whereas if the decisions are constantly made for them, they may take longer to be able to make their own decisions.

There is no right or wrong answer to that question.