Ok, your SWH actually made some sense - I couldn't tell from your original post whether this were two children with different needs. I do still stand by my answer: trying to "break" a child is NOT the right thing to do. If you have taken Psych and early development classes you should know that. I do not know of any physicians or child development experts that advocate letting your child scream for an hour and a half until they throw up! Even "crying it out" proponents would consider that just cruel.
If his pediatrician thinks that he needs early intervention he should prescribe occupational therapy for him and the therapist can teach you and his parents how to deal with these issues. What you are doing is very apparently not working and you need help... I would suggest that that should be professional help.
Good luck!
So just so I get this right: you are a nanny or a sitter for 2 toddlers: one is 12 months old and one is 20 months old?! Right?
And you have trouble with BOTH of them?
If your tried to "break" my baby and let him cry for an hour and a half I would fire you! Immediately! Do your job and care for this child - this means rocking them to sleep if you have to, that's what you are being paid for!
If you are truly concerned, you have an open conversation with both sets of parents about your observations. The 20 months old may need to be evaluated for sensory issues or other developmental needs.
The 12 months old sounds normal. Many babies go through a phase of separation anxiety at that age and letting them cry until they throw up is NOT going to help!
If you cannot handle the responsibility of caring for two toddlers please quit and let them have a nanny who can. Childcare is not for everyone - I mean I couldn't do it... there is no shame in recognizing that a certain job just isn'y for you. If you do really want to continue please take a childcare or early childhood development class! You will get better insight in what is normal and what is not and you will learn techniques how to deal with challenging behaviors.
Good luck.