When Mojang made Minecraft 1.9 they changed the riding packets (the way the client interacts when riding entities; AKA horses, boats, minecarts, etc.) so when riding an entity in 1.8 vs. 1.9 the movement is different, producing that if you are playing on a 1.9 or higher Minecraft client in a 1.8 server (HHG as it is now), the client would express the movement differently than the server, so both movements would be asynchronized, causing weird stuff like the events you recently narrated. Therefore, unfortunately, the only way to fix this version incompatibility problem (it's not a bug technically), would be to force update the server to 1.9 or higher, which isn't possible right now as majority of the player base are still using 1.8. Nevertheless, I suggest you to temporarily use Minecraft 1.8 when riding horses or other entities in the server in order to avoid experiencing this problem. Apologies for the inconvenience!
