If I check my baggage at Idaho Falls, have a layover in SLC, then SLC to Seattle, Seattle to Shanghai do I only have to check my baggage once, at IF, or do I have to collect it from the carousel and transfer it myself? If I do have to is a 2 hour layover in Seattle enough time to do so? Beginning with Skywest but it is a Delta partner.
Unless you have a change of airlines, you should be able to check your bag all the way through.
On the way back, assuming a round-trip ticket, you will have to reclaim your bags in Seattle, go through customs, then re-check them again. Although there will be no additional cost in doing so.