I assume the "extender" is a length of coax and a barrel connector? Not a short item that looks like a barrel, but is an attenuator? If "extender" is splitter/combiner into the other room, mention it.
Anyhow, if Remote 2 is 6.2/6.3/6.4, you'll get added range by changing the switch below the battery cover from A to B range. With receiver at Menu-Menu screen (SysInfo by lots of methods), change to B range and hit Record. But that will prevent use by any 6.0 remotes. If Remote 2 is a 21.0, Odd addresses are A range and Even addresses are B range. I don't have a 21.0 to say if they work better in B range, but worth a try.
Anyhow, if Remote 2 is 6.2/6.3/6.4, you'll get added range by changing the switch below the battery cover from A to B range. With receiver at Menu-Menu screen (SysInfo by lots of methods), change to B range and hit Record. But that will prevent use by any 6.0 remotes. If Remote 2 is a 21.0, Odd addresses are A range and Even addresses are B range. I don't have a 21.0 to say if they work better in B range, but worth a try.