Would making a blockchain that has the difficultly target 1 week be too long for any reason?
Too long for what? For an interplanetary currency with miners as far away as Eris? Sure, one week sounds like a good target. Maybe even two. Call it ten Earth days. The speed-of-light delay would make anything shorter than that infeasible. However, we don't have an interplanetary economy, and nobody here on Earth is willing to wait weeks for confirmations, so I'm not sure what you're trying to accomplish.
I'm thinking that maybe issues with miners getting off and online would cause problems?
No. Why would it?
Is there someway to use smaller blocks but throw away all of them except for the ones that are one week apart?
No. Timestamps can be faked. Only the block hash can determine if a block is valid. This means that you will occasionally get blocks very close together, resulting in orphaned blocks from miners on distant planets. This is unavoidable and happens with Bitcoin, too (except for the part about distant planets, obviously).