If my husband is 12% owner of a sub-chapter S corp and his business “partner” bought a 2nd business which is a competitor, does my husband have any recourse?

Your husband might have recourse: a majority owner of a privately or closely held company has a "fiduciary duty" to not deliberately or carelessly damage or devalue his/her minority partner's investment. However, the majority partner is allowed to engage in his/her own business ventures if they are reasonable ones, even if they turn out, in retrospect, to damage the minority's partner's interests--that is, it's (so to speak) the intent of the majority partner's actions more than the specific acts themselves which determine if the fiduciary duty is violated. Also, if there is no harm, there is no violation. So to go over a few scenarios as examples:
1) The competiting business already existed and the majority partner simply runs it completely independently of the businss your husband is involved in--nothing changed  but the ownership of the competitor, so the other partner did nothing wrong; he/she did not act to increase the harm (if any) the other business suffers from competition. No breach of fiduciary duty.
2) The other partner bought the business with an eye towards consolidating it with the first business in some way, which will yield a single business with greater market share and lower costs--even if that doesn't work out, it's a reasonable plan for a business owner (look at how many Fortune 500 companies do this) and so no breach.
3) Similar to the above, the other partner intends to not formally combine the businesses, but to run them in way (sharing back-office resources and investments, plus expertise, for example) that leverages investments to help both. This may or may not work, and one business may benefit more than another, but again, it's a reasonable plan that many companies follow. No breach.
But contrast that with:
4) The other owner buys the new business and shift his time, attention, and resources from the business which he "only" owns 88% of to the one he now owns 100% of. The sharing is one way only--he takes, for example, customer lists or vendor contacts from business 1 for the benefit of 2 and not vice versa, and starves 1 of attention and money while he's growing 2. That would very likely be a breach of fiduciary duty, since he is hurting his minority partner's interest to benefit his own.