I have no advice on the potty training. I was one who finally "gave up" when my son was uncooperative. Took a break for a month or two and came back to it. It truly saved my sanity. BUt I resisted for a long time, so I can completely understand where you are coming from in that regard.
For the sheets, my four year still isn't totally night time potty trained (Much to my frustration and disappointment). I have learned to double sheet her bed. I have a waterproof sheet on her bed a sheet, then another waterproof sheet and the regular sheet. Now, I still have to wash everything immediately, so the house doesn't reek, but with the double layering I don't have to make the bed every day...it gives me a bit of a break.
As for the "into everything". I can totally relate. Both of my kiddos were like this, but my youngest was by far the worst! She was a climber. She was into everything. We changed some things to help save everyone's sanity and keep the kids safe. These changes were not always ideal, but they worked and for the most part, were temporary.
We locked doors. For a while her bedroom was the only thing left unlocked. It was a hassle, but it beat a mess being everywhere for sure!
We have a great room, there is no way to keep the kids out of the kitchen. So we modified the kitchen. Kid locks on all the cabinets (we went through two or three brands before we found one she couldn't get into). I made a few spots accessible to her. We put tupperware in a drawer and dish towels in another. The kids could plunder and play until their hearts content. Yes, it meant washing any plastic ware before use, but I was ok with that.
There were days, where I literally dragged the dinning room chairs to the back porch. Just to have a day or two where she wasn't climbing on the table. Our bar stools had to get temporarily moved to our bedroom. (Hubby was concerned the weather would warp them in the garage or outside). We couldn't keep the kids off and found them on the counter walking around...not safe.
We also learned to keep our kids busy. Productive kids are usually behaving kids. I had some "go to" activities and "go to" places to go. Sometimes it was as simple as a walk down the street pulling the wagon looking for "treasures". Play dough was a life saver. At that age we'd give them one of the small party tubs and let them go to town. Glue. A bottle of glue and pasta or cotton balls or paper bits...could occupy a kid for a while. Have a "stash" ready to go. We also included our kids when we could. When I cleaned the bathroom, my kids would get baby wipes to use to "help" clean. My daughter still likes to "help", you just have to get a little creative, so that you are not working around the kids too much.
I would encourage you to continue with time outs. It will take a while for her to "get it". There will be days where she will wail and days she will act like she doesn't cake. Make the spot some place where you can see and watch her, but she can't participate or see the tv. Stick to it and eventually it will make sense, but it does take time.
Hang in there mama!