Don't worry, there is nothing wrong with your remote. The remote for the 6100 will not work with your 3100 or 5100. I have all three of those receivers as well.
And I have two remotes for both my 5100, and 6100 (dishnetwork equivalents that I ordered online).
The 6100 remote is the UHF Pro 8.0 remote. This remote only sends UHF Pro signals when in SAT mode. The IR is for the other devices only. Hence it cannot control your 3100 or 5100 through IR.
Further, UHF Pro remote operates at different frequencies than the original UHF remotes which your 5100 has. That is why it cannot control the 5100 through the UHF signals it sends when in SAT mode.
Although it may be a dissapointment that you can't control your PVR, I must say that the UHF Pro seems to work an order of magnitude better than the original UHF. With my 5100, I never really could get it to work reliably using the little antenna that was shipped with it. Now I have my PVR antenna jack connected to about 150 feet of coax into my basement where I have a Radio Shack UHF attenna. That seems to work for the important rooms in the house.
With my 6100, I have the little antenna that came with it attached on the back and it works perfectly from anywhere in the house. The UHF Pro works way better than the normal UHF on my 5100 - a much needed improvement!
If you want a second remote that is like the silver one that came with your 6100 yet does also send IR signals so you could use it with your 5100 PVR, then try ordering a Dishnetwork UHF Pro 6.0 . The UHF portion obviously won't work, but I do think it will work via IR in SAT mode.