I just got done with a trip out to Yellowstone and Grand Teton National Parks a few weeks ago. I had the same dilemma as you. I ended up renting the 12-24 and the 60-250. I already owned a tokina 28-70/2.8, 18-55wr, and dal 35 as well as the k5 to attach it all to. I carried this all in a Lowepro SlingShot 202 AW and didn't think it was too heavy. I think you'd be fine split between the two of you.
Definitely get the 12-24. A wonderful lens to capture all the geysers and hot springs with. At times I wished I even had wider! I'd consider a good wide angle a must at yellowstone.
As much as I loved the 60-250, sometimes I wished for more length. I think the da*300 would be a good choice for you. Maybe you should consider switching out the 50-135 for the 60-250 just for the added versatility. I don't think you'd miss the 1 stop advantage of the 50-135.
Mostly I found myself switching from the ultrawide for the static scenery, then we would spot some wildlife and I'd have to quickly change to the longer lens. Having 2 cameras would have saved a bunch of hassle.
Most of all I'd encourage you to spend more than two days in the park, especially if you want to do some hiking in different areas. It really is a huge place and the time it takes to travel between areas of the park is misleading. I spent 4 full days in the park and could have spent many more hiking to different areas. I also spent a day in Grand Teton park and wished to have spent at least another day there, too.
These guys will be waiting for you I'm sure...