the OP is right to be uncomfortable about the hrose walking directly behind her. this is not good. should the hrose be spooked and lunge forward, he will step on her.
To be fair, a horse can spook from any direction and cause the leader harm if the situation has the right number of factors.
Yesterday I was leading my mare from the pasture to the barn, and she spooked at someone getting out of their car. In this situation, I was leading her properly with her at my side, and she ended up sidestepping into me and her hoof made nice solid contact with my foot. There was no way to avoid this, given the parking lot is circular and so therefor we were surrounded on all sides by cars. This is normal on a busy day at the barn. I don't get to pick and choose my surroundings and the world doesn't revolve around me and my horse. Accidents happen and it was no one's fault.
But I do understand that, OP, you would rather have your horse at your side. Your horse may not understand that you want it there - so you need to make it clearer.
I am going to try and get my thoughts collected to explain what you could try, bear with me. This is how I trained all three of my horses to lead beside me... Sorry if I fail to put this in words that are understandable.
1. Introduce the idea of walking beside you.
Start by standing next to the horse at the shoulder. Point YOUR body forward, just like you would if you were leading. Take a step forward and, while doing so, ask the horse to move on or step forward as well. You can do this by standing beside the horse and pointing your lead rope forward. Use a crop, whip, or your other
arm to drive the horse forward at the shoulder if it does not move on cue. This reinforces the idea that when you walk, the horse should also walk and that the two of you walk side by side always. I assume your horse already has a basic understanding of this, since it leads behind you. Soon your horse will be a pro, and will understand that when your leg moves forward, that its legs must also move forward!
2. Correct unwanted behavior.
If your horse starts to drift behind you (this is expected since it thinks you want it to follow behind), immediately correct it. If your horse moved behind you, take the arm you are carrying the lead rope with and OPEN IT OUTWARDS, asking the horse to follow the direction the lead rope is pointed. The idea is, if you point your lead rope in a certain direction, the horse will move into that space. Open your arm to the right and the horse should move to the right, effectively coming up beside you. This is a useful tool in any leading situation. You should just be able to point and ask, and your horse should go.
If the horse does not move in the desired direction, then the horse doesn't understand and you need to make it clearer. If opening your arm does not work, add the whip or crop at the shoulder with your other arm to drive the horse in the direction you want. Remember to keep your leading arm open in the direction you want!
Do not forget this if you are driving the horse forward with your other arm. Your leading arm must also be asking
. Eventually, you want to be able to simply point and the horse will move into the space you want. This will even help when you need to train your horse to lunge! I am going to post some pictures to help where words fail... Give me a few minutes as I have to do this on my other PC.