Re: lawsuit
In general, agreements including lawsuit settlements whereby anyone is restrained from engaging in a lawful business, trade or occupation are unenforceable as contrary to public policy. There are a couple of rather narrow statutory exceptions, where the sale of a business includes goodwill or in the breakup of a partnership where goodwill is part of the property divided.
I mention this because many people in addition to the asking party read questions and answers on LawGuru, and it is not 100% clear from your post whether your use of the term "partner" refers to a business partner or domestic partner.
Assuming this was a business situation, I would start with the notion that the covenant to refrain from "doing business with" the hospital would be broad enough to include accepting employment, and also that the agreement does not violate state policy and is enforceable.
Based on the limited information given, I'd guess this result is about 60% likely. However, due to the 40% or so possibility that a result in court would be more favorable to you, if the job opportunity is important to you, I'd definitely recommend seeing a business lawyer in person to have the agreement interpreted based on a full reading of all its terms.
I also like the idea of trying to negotiate a waiver of the covenant with the other party to the agreement.