It isn’t illegal or, in my opinion, unethical for the spouse of a board member to provide services to a nonprofit organization.  The legal question is whether the compensation is reasonable and the spouse who receives unreasonably high compensation from a 501(c)(3) charity or (c)(4) community or advocacy organization could be subject to excess benefits tax.  (See Ready Reference Page: Charities Must Avoid Excess Benefit Transactions”) 

Unless the funder of a project requires bidding, the ordinary private nonprofit is not required to bid any part of the project, although it is clearly a good idea for major purchases.  Even though it is not illegal or necessarily unethical to hire a spouse or even a board member, construction projects are particularly susceptible to insider benefit even with a bidding process.  Selection of design is clearly subjective and a bidding process could be a charade.  The bid price for the actual construction could appear to be “objective” until the change orders start coming in.  In the end, you have to rely on the integrity of the organization in dealing with insiders who supply services to it.  You can increase the likelihood of a good outcome with a strong independent project manager who oversees the project for compliance.