If the husband owns the business solely, and all the paperwork is in his name, I don't think the wife should apply using the official business name or EIN. The reasons being, (1) to apply for a card for a business, you need to be an authorizing officer: an owner, partner, member, president, vice president, or treasurer -- not just an employee; (2) if the wife applies for the card using the official business name (that doesn't match her legal name), Chase will want to see some documentation of her name and position with the business; (3) if she applies as a sole proprietor, it can't be with the business name -- it has to be her full name or it'll get flagged and go back to #2; and (4) if she applies with the EIN and not her SSN, Chase checks the EIN and will see only her husband's name on it.
I don't really have much experience with businesses owned by one spouse, but the other spouse applying for a business card using that business. I know there are some here who have done this. Don't rely on me for this, but I think they just applied as a sole proprietor, in their own legal name, using their SSN, but otherwise using the actual business's info for type of business, revenue, etc. It'd be more straightforward if the husband applies for the business cards since his name is on everything.
I would suggest one of them get the CIP now, then refer the other down the line whenever they're comfortable with the spend. Getting the CIP now would put about 3 months between now and mid- to late-December, when you're planning for one of them to go for the SW Biz.
As for why the husband should get the CP first,vs. the wife? That sort of depends on how they want to time their apps with at least 90 days in between business card apps (to avoid risk of denial or shutdown by Chase). If the husband goes for the CIP now, in 3 months he could go for the SW Biz and start chasing the CP for next year and 2020. If the husband gets the CIP now and refers the wife for her own CIP in October or November, that means the wife shouldn't go for the SW Biz until January or February. Also, again, you said you think the wife has a SW personal card already. She'd need to cancel that card before applying for another SW personal card.
(If the wife isn't comfortable going for biz cards in her own name, she can always go for the CSP or CSR, which the husband can't refer her to and has a smaller bonus than the CIP -- but still, 50,000 UR! However, since double dipping 2 personal SW cards is dead, the only way for her to eventually get the CP is by doing 1 SW Biz+1 SW personal card.)
