That might not be what Russia wants, but do ya think they will turn down the help? What about what we want was our sanctions put in place so China could offer to help them and give them a end run around our sanctions?
As far as Russia and China's individual goals as separate nations that don't have to be a death sentence. Us and the UK has separate goals and we are chummy as heck. Yea I know now ya say well they are not the US and the UK. Honestly they could end being just as chummy as they have a common cause between them the US and they went as far to form a alliance called the BFF alliance just like they are a couple school girls texting.
The U.S. and U.K. are chummy because we're not competing for something that cannot be shared. For a while we were, and we were very much not chummy, it was when we stopped that we became such close allies. Putin may accept the help, he may not. He's a very prideful person and holds a lot of influence over his government, where appearances are nearly everything.
I'm not sure what you think we should have done, gone to war? Over Crimea? That would be an awful move politically. Nothing? That's not smart either. So we hit them with sanctions, and start to assimilate with his neighbors, and bring our western culture to his doorsteps. Much like we did in Western Berlin, we put on a show for those on the East, just because it was right there. There's more than one way to punish a country for aggressive actions, and we're exploring one way that will likely get to Putin on a personal level.
Make no mistake though, going to war and forcing Putin out of Crimea would be an awful choice. Crimea is home to one of Russia's very few warm water ports (meaning they can use them year round), they have less than 10 I believe, and the only one that allows them to monitor that region well, home to one of their fleets which they see vital to their national security. That's a big deal to them.
Imagine that Hawaii was actually their own country instead of the United States, but we still had Pearl Harbor there, so they allowed us to use it freely. Then one day they start to get chummy with North Korea and agree to enter into a trade agreement with them and open up travel and assimilate with them. We're not happy about that obviously, so we put pressure on them to come back to us. When they do, protests break out and suddenly people throw out the controlling leader to continue with the move. So what do we do? Risk losing the port and access to the region? Now imagine Pear Harbor is the only port we have availabile (which really it is for right there, but for sake of the analogy let's say we don't have ports on the West coast for whatever reason) so what do we do?
We go and take control of O'ahu to protect our port, and thus our defense. Now imagine China comes and tries to kick us out via military force, do we let them? Do we let them park themselves right at our back door, kick us out of our old port by force, and let them force us to lose our ability to monitor the region? Fat fucking chance we do, we buck up and get ready for a fight. Especially if China is just getting out of some long wars and the population doesn't seem to have any desire to fight another potentially very costly war, we estimate their resolve isn't that high, and hopefully putting up a fight will keep them from really committing heavy forces.
Using force likely gets a strong reaction, hardly worth it for a port/ region that we don't really care about, and our ally was looking to increase relations with. So its far smarter to look at alternative actions, sanctions, especially given their extremely optimistic economic projections (unlikely to come to fruition), and a volitile population, look like a better option at this time. If China steps in to help them, then that's part of global politics. That still won't let Russia create a Eurasian Union, or increase their regional power, or create another bipolar political environment, all of which are Putin's political goals.
War however, even though we would ultimately whup their asses up and down the globe, would be extremely costly, and the risk of going nuclear would be very high. Any leader who rushed into that fight would be a fool. Which is why nobody is doing that.