Fareastdriver,
Your description of what you are looking to achieve is somewhat confusing.
Do you want to
use the wireless mouse from the other side of the room
In which case, the answer is as Mike-Bracknell says, get yourself a better wireless mouse (a Bluetooth one rather than one that uses another form of wireless .... and if your room is so big that Bluetooth doesn't work, then quite honestly you can probably afford a bespoke solution !)
or do you want
a two piece monitor plug in much the same way as a keyboard or mouse?With this one could leave it in the TV and fire it up with the laptop as required.
i.e. a splitter ? They definitely do exist, you just need to know where to look.