If you isolate the hen, that means you lock her in a crate, cage, whatever, where she has a nest, a food and a water dish, and enough room to go poo when she needs to without getting it in her nest. If you don't lock her up, the other hens can get in the nest with her and lay eggs. Some broodies have been confused when they leave the nest and another hen is on their nest when they get back and gone to different nests. When you first move her, she will go back to her old nest unless you lock her up where she cannot go back to the old nest. After a few days, she might accept the new nest and stay in it if you unlock the door, but I would not risk it.
If you do move her, keep her in the new cage at a could of days to make sure she stays broody brfore you give her any eggs. Sometimes they will quit being broody when you move them.
I used pencils to successfully mark eggs when I was growing up on the farm. I didn't write anything on them, I used a soft leaded pencil and rub broad bands around it. They might fade a bit but I could easily see them when I check for new eggs. I am not aware of any harm that a sharpee will do if you use it to mark the eggs. I would like to know what the harm is. A sharpee is now my preferred method for marking an egg.
If you do get two broodies, it is important to mark the eggs differently.