Ahhh the perfect all in one lens.... 18-300mm f2 and in the size of a 28-300mm ... A guy can dream right?
You covered allot of different situations and almost all of them you are looking into prime-land. 1.8s and 1.4s are your friends. Need a camera with a motor drive for sure. The key for low light is getting a sharp image - you can always crop to get some extra distance for the frame.
What I use:
Landscape - Everything and anything
Wild life - 70-300mm VR - 70-200mm VR with 1.7TC
Sports indoor and outdoor at day and night - 70-200mm VR, 50mm 1.4 & 85mm 1.8 - day you can get away with a 70-300mm VR. I probably use the 85 the most to keep the ISOs low.
Performances on stage - 35mm 1.8, 50mm 1.4 & 85mm 1.8
$2,000? 50mm 1.8, 85mm 1.8 & 70-300mm VR would be the best start since you only have two other lenses and it would complement them. Add some great software for Noise Reduction (Nik, LR3, Noise Ninja etc) and an Expodisk for WB and you have a winning combo. The 70-200mm VR would be the next step for sports.