Your lawyer works for you and therefore has to act on your instructions and if she refuses get a different lawyer. Do not settle stick to your guns when it comes to your children's safety. You are right to demand that he undergoes all of these tests to prove his sobriety to ensure your children are safe in his care and so that you can relax when they are there.
I'm not sure about withdrawing until your at the point of a final hearing and I certainly wouldn't agree to an agreement he can breach that at any time. What you have is a court order I think which holds more power. It will also show the judge between now and your final hearing how committed he is and whether he has breached it. Keep the order you have
I am sorry you are going through this take care