OP, he's away from you for five days a week. You're his mum, and at three that's a long time to be away from your mum.
The constant attention seeking may be because he's afraid you'll disappear again.
The problems with bath time - he knows that means it's nearly bedtime, and he doesn't want to go to bed, he wants to be with you.
Reading to him - again, he wants to be awake and with you for as long as he can, so he only goes to sleep when he's too tired to stay awake.
In the morning - he knows that getting ready means that soon you'll be going away and leaving him so he cries and tries to put it off for as long as possible.
He'll be the same at the weekend because he's too young to understand that for two predictable days of the week you don't leave him, and so is just waiting for it to happen.
Right now you're weary and drained and fed up so it may not be what you feel like doing, but can you forget the teeth, bath etc for a few days, and concentrate on reassuring him? When you see him in the afternoon, make a really big fuss and tell him how thrilled you are to see him again. Before you go to work spend the morning telling him that you'll see him soon, and that you'll do x/y/z nice thing with him and how much you're looking forward to it? Can you facetime him at some point during the day, maybe not when he's at nursery but when he's with your parents? Say hello, ask him what he's been doing, tell him that you're thinking about him and missing him, you'll be there soon and you love him. At the weekend, start the days by telling him all the nice things you've got planned so that he knows you'll be there all day?
He'll then start to understand that you haven't gone forever, that you will be coming back. At the moment, it sounds like his fear is that once you're out of his sight you've abandoned him for good.