It is somewhat known that most areas have some sort of scaling mechanic. If you have a quest that is quite difficult it could be a number of things:
- The game's difficulty setting
- The level of the skills you are using affecting how well you can do combat
- the scaling, when combined with the difficulty setting, has made the enemies much too difficult
- The equipment you are currently using
- The combat strategy you have been using has been inefficient and it hasnt been a problem until now
Try setting the difficulty lower and see how low it needs to go before it becomes managable. It may just be that the scaling for that quest is off.
I've had success with a few things when it comes to people following me. I'm not on a sneaky character, so I've had to get crafty for some missions. It sounds like you've tried some of these methods already, but I'll put them here anyway just for completion's sake.
One is to try during the day, when people are out and about or tending to their stores. I've noticed that some (not all) vendors will stay at their counters instead of following me.
Second, is to go in and scout a quick path while letting the person follow you, but not steal anything. Then, go out and come back in (this usually resets their position) and make a mad dash for whatever you needed to get. I may just be lucky at encountering slow people, even in Solitude. I'm not sure if their speed or concern with me stealing something is related to anything.
Finally, I've also had success with telling my companion to wait on the stairs or in smaller door ways to block the person from following me, or at least slow them down more. It seems to be hit and miss, but it's worth a try.
I've also read (and it's mentioned in a comment above) that buckets/pots on heads can work. I've never tried it myself, but it would be a lot funnier than any of my suggestions! Maybe some combination of buckets and companion blocking to slow them down would help.
Best Answer
As Raven Dreamer notes in the comments, the Skeleton Key is an unbreakable lockpick: that's pretty much its only purpose (and a fine purpose that is!).
However, if you want to continue on with the quest chain, you must return the key to complete the quest. But be sure to take out as many locks as you have before you do!
But however, what you can do is keep the Skeleton Key until you get Lockpicking to 100 and got the perk Unbreakable. This will allow lockpicks to not break when you're attempting to pick the lock. After you get the perk, return the Skeleton Key to Twilight Spechuler.