It isn't mechanics trouble or bad AI, it's user error, I did this the first time too, easy mistake. They have to have equipment equipped just like you or they can't do what the missing equipment would let them. In this case, that would be a fishing rod. Also, the girls start out intentionally unable to do things because they canonically don't know how. They will learn over time, but you will have to be ready to treat conditions like exhaustion, where they collapse and you have to carry them to a bed. The easier way is to have them follow you and do things like sleep yourself while they are following. Inability to cross the river or get under the tree is not a problem because you can teleport to base, go to the map and click the red flag. Any that you have a base at will pop up a Yes/No prompt and selecting yes will send you to that base. Also, giving food to the girl does NOT have her eat it, she will see it as any other gifted item and put it back in the storage. She will only eat from cooking storage, which can be accessed from any cooking furniture except the campfire.