I think you are doing great so far, Tina! Well done.
From a puppy point of view I would ensure the bucket is cleaned throughly after every meal as I assume lambs are as prone to infection in the early days as any other animal.
If the bigger two aren't taking the bottle then they are getting enough from Mum and you can just feed the wee ones. but I would leave them with Mum too, in case they are getting a little extra from her as well as the biggies, and also from the point of view of socialisation with the rest of the flock when they are integrated.
Is there any inconvenience in continuing with the warm milk? I'm sure your sitter will be happy to do that too. I would keep them on warm till you come back then wean them slowly onto cold milk, but as I said before I know nothing about sheep - only puppies.