Multiplayer Server chunk/lag/chat errors

When playing in a multiplayer server through Hamachi with just one other person (who is the host), I experience huge amounts of lag when first joining (which is pretty normal). I fall through nothingness, then land inside of a block underneath the surface with a crunch like I've taken damage. After a while I will appear on the surface and sometimes, after a while, I will stop lagging (again, pretty normal).
However, recently, weird things have been happening. I'll send messages that will appear in chat to the host the time that I send them, but I will be unable to see my own messages, or his messages until about five minutes later. I am almost constantly "moving incorrectly" even when all I'm doing is turning around. The hunger bar still drops and it is possible for me to move around for a few minutes but eventually I will be put back to where I begin/put back to where I was a few minutes ago (server says I moved incorrectly). I walked to the edge of a chunk and nothing else loads, it's just a huge drop off that's completely black (I was too scared to walk beyond it because we're in hardcore mode). What's most odd is that after a while, even though everything moves smoothly for the host, we will both be kicked off the server. We were playing in this world the same way two days earlier and it was perfectly fine. Neither of us have any idea what to do to fix this.