Dear pgf: There is no single "right" answer here. Both methods, local control followed by chemotherapy and chemotherapy followed by local control are accepted options. In this situation, given the size of the original tumor, we would likely recommend chemotherapy first (neoadjuvant chemo) - address the systemic disease and follow with surgery. If the margins after surgery are positive or close, then radiation "might" be considered.
Studies of how to handle this specific timing are few: it's fairly uncommon to present with an axillary metastasis without finding the primary. In general, when it occurs, it's felt by most that the breast treatment ought to be mastectomy: radiation of the breast supposes removal of the primary, and an extra boost of radiation to the area where it occurred. When the primary isn't found, then radiation to the breast would not include such a local boost. So, ultimately, if it were my patient, I'd suggest mastectomy. However, as you suggest, the timing is a major issue; since the known tumor was removed, I'd be inclined to go for chemo now, and surgery later. So my feeling is different from either of the doctors you mention: chemo now, then mastectomy. The choice of reconstruction or not, by what method, and whether to do it all at the time of the mastectomy can be decided later. Please also understand I'm an experienced breast surgeon who chimes in here, but I'm not offically associated with the site, and there will be an answer from them, presumably Monday.