So you are wondering how to train both Olympic weightlifting as well as kettlebell lifting. Is there a balance that can be met? Well, if you are trying to seriously train for either sport, then in my opinion, no. One has to give. Sure you can use the other as a compliment to your training, but it has to take a back seat and it has to be of relatively low intensity.
Each of these sports hits the central nervous system in different manners. And when training at high intensity, one needs to give their body a chance to adequately recover. Simultaneously training for each of these sports won't allow that recovery to happen.
At the moment, I can focused on Olympic weightlifting. Personally, after a training session with heavy barbells I have no desire to start lifting a kettlebell, or two, for long sets. First, my body is already fatigued. Second, my hands are usually already feeling like raw meat. Neither of these bodes well for kettlebell training. So what do I do?
I now use kettlebells as a means for conditioning. I typically pick up the bells on the days I am not training the Olympic lifts. I will train for long sets but with lighter bells. I may also include this bell work in conjunction with some other conditioning work.
Extended set of kettlebell swings: Swings are relatively easy on the hands. Depending on the weight used, I may alternate hands every minute and swing for a long set. For example, I've performed a 10 minute swing set with a 16kg bell, switching hands every minute.
Circuit of kettlebell swing and jumping rope: Perform a 2-minute set of kettlebell swings (1 minute per hand) with a heavier kettlebell, then move right into a 2 minute set of jump rope. Then rest for a minute or two and repeat. A few circuits of this works one pretty well.
Half Turkish Getups: For some core work, I have started introducing these into the mix. They are easy on the hands and work one's core pretty well. If you want to superset with ab wheel rollouts, go for it.
Extended set of kettlebell snatches: For days when my hands are feeling good, I'll perform an extended set of snatches with a lighter bell similar to the extended swing set. Focus is on breathing and technique. The last thing you want to do is tear your hands up. Especially if you are scheduled to pick up a barbell the following day. If you perform you snatches with proper technique, you will not damage your hands. This should be avoided particularly when training.
Personally, I am still experimenting with what works best for me. I try to be flexible in my exercise selection. I may also play around with light clubbells, medicine balls, "battling" ropes and box jumps. Whatever you choose to play with, just make sure you have fun with it!