While you can spread it from your hands to your eyes, it is highly unlikely that you'd spread it from your hands to your kids' eyes unless your hands are going directly from your genitals to their eyes.
You won't transmit it to their genitals unless you are having inappropriate sexual contact with them.
Were you tested during pregnancy? If you were, and you're positive now, that means your boyfriend has had a new partner since. That's definitely something you need to think about. He's having other partners without protection.
Hi, and Sorry you got Chlamydia. Both you and your boyfriend need to get treated or you will keep getting it. In the meantime you need to wash your hands well every time you use the bathroom or touch you or your boyfriends genital area. It can be passed from hands, and genitals to eyes (which can cause blindness) and genitals of your kids. If you both have been treated then you need to both test negative after finishing the antibiotics. Hope this helps.
mkh9