Pitch Runner substitution

LL allows re-entry of a starter in any place in the order, with some restrictions on playing time etc.
Not like most re-entry rules, where a starter must re-enter in their original spot.

Also a rule for injuries which allows the just removed player to re-enter at the time of the injury. Most, if not all youth leagues allow for substitution of an injured player even if no eligble players are left, but, if memory serves me correct the selection of the player to re-enter is reserved to the opposing coach. With only ten players, not much option.. Sorry I can't quote rule and section, been many a year since LL.

It may have been a while but you are correct. Normally a starter may return anywhere in the line-up after his sub has met 6 defensive outs and one AB. With an injury with no illegible subs, the opposing manager may choose the replacement. As jjk says with only 10 players not much of a choice.