Range extenders only allow you to use the remote a little farther away, but will not go through walls or doors since they are still infra-red. You will not be able to do this with the 3100. At least I don't think you can, but if anyone knows of a converter that will work with the 3100 the information would be welcome.

You could use a universal infra-red remote with radio frequency capability, like the OneForAll URC-9910, which sends IR commands to an RF transmitter which sends them to an RF receiver which converts them back to IR.