Your wife's care sounds on-target so far. My wife was also referred to a major treatment center from our local hospital, where her treatment with ATG and cyclosporine was started almost immediately after we met with her new hematologist.
From the reports we hear in these forums, ATG treatment usually goes smoothly, although it's sometimes necessary to adjust pre-medications or the rate of infusion after the first treatment, to minimize allergic reactions. The treatment is not likely to produce instant results. Instead, you look for blood counts to trend upward during recovery.
I hope it goes well for you.
Founder of Marrowforums and caregiver for my wife