I tried to unit and join the end anchor point with the path shown in the picture but I either get the paths interlocked or part of the drawing just disappear.
You can't merge it with a path. You can only join anchor points to other anchor points.
Anyway, there is no need to do that. There's nothing wrong with the paths just the way they are in your example. If your ultimate aim is to colour in the drawing, learn about the Live Paint functionality in Illustrator - there are tutorials online.