That's great! Belly breathing is a core component of natural health. It's also emphasized in Egoscue, Edgelow, yoga and tai chi.

Overall the video was nice, but at the end she mentioned that breathing was done by expanding the rib cage. Unless you are engaged in physical activity (which would include pilates) all your breathing can be done with the belly; there is no reason to engage the ribs, scalenes, etc. during most of your day.

For example, consider the comment "Evaluation of the patient’s respiration demonstrated a faulty breathing pattern, involving over-utilization of the scalene and SCM muscles" at http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1769463/

Congrats on making progress.