I wouldn't worry too much about coyotes. Generally, unless they are starving, they wouldn't even attempt to go after a full grown, healthy horse. They are very shy by nature too, and will avoid humans if at all possible. We have quite a few of them around here, you can hear packs of them howling at night, but in all the years I have ridden back in the woods and around the river, I have never seen one. In fact, I've only ever seen one at all, and that was one that was crossing the road as I was driving.
Get some pointers from your neighbor, ride with him if you can, to build your confidence level, and even if you don't feel confident around the horse, try to move and act as though you are. One other thing, when you are out riding, don't just be a passenger when it comes time to go home. That could encourage other bad behavior that you don't want. It's never a good idea to just let them go home whenever they want to, even if they are acting up a little, that will quickly lead to a barn sour horse. I'm not saying don't go back home if you feel unsafe, I'm just saying make it your decision to do so, go at your pace, and the way you want to go, and expect him to act accordingly. This may very well require someone with a little more knowledge, at least at first, if the horse has figured out you are unsure of yourself.
"Keep a leg on each side and your mind in the middle"