I wouldn't do a double time out for someone so little. I think pick your battles is a good strategy, it seems to me that the undressing on the chair is an attention seeking thing so might muddy the waters when you are trying to discipline something else so I would ignore it personally and just redress her as Clover suggests. It would be tricky to do the three warnings when she is already on the chair and would be very confusing.

Remember that part of the punishment on the naughty chair is not getting mum's attention.

With the chair movement, how about get rid of the naughty 'chair' and get a naughty spot. You could use a cushion, bean bag, stair or something else. That would save the floor. If you want to avoid her moving to another area, maybe you could use masking tape to mark a spot on the floor and ask her to sit in there. I always try to remove the chance to do something naughty where I can, then you can control things more IYKWIM.

It is really tough to work all of this out, especially when you are pulled in so many different directions with a house to run and a new baby.