MacBook has poor Bluetooth range

No, this isn't normal. Considering the age of the machine, I'd guess that it's a failing Bluetooth card. It could also be some sort of interference.

If it is really a case of poor Bluetooth range and not any interference. It might be that the Bluetooth antenna is loose / disconnecting from the Bluetooth card causing poor reception. Might not be a bad idea to double check the cable and make sure its connected and not corroded, etc. Before replacing the Bluetooth card.

If you are a DIY'er here is some more information on disassembling your MacBook see iFixit's guides for MacBooks. Other wise take it to a Apple Store or an Apple Authorized Service Provider for help.