I assume the reason you setup a corporation for your software development business is for some limited liability protection. In other words if some software you wrote malfunctions they may get the corporate assets but not your house.
Clearly a company can have multiple lines of business, big conglomerates do it all the time. There are however often substantial benefits in keeping unrelated lines of business in separate companies. In your case if you have only one company and you get sued, then you end up loosing two businesses, yours and your wife's since they are one company. If on the other hand you have a company and she has a separate company and something happens to one of them, the other, being separate, will be unaffected and can continue.
Another benefit of separate companies is if you ever want to attract investors or sell the business. You state that your wife's business is completely unrelated. Suppose for example that she bakes and sells pastries. Now five years down the road a big company wants to buy her baking business. If you only have one company it is highly unlikely that they will want the software side of the business, thus making it more complicated to reach a deal. To understand this consider what happens when they want to review the books and records as part of due diligence, they will need to separate out all the software related transactions from the baking transactions.
The only benefit I can see to using just one company is if your wife's business is just occasional and infrequent and can't justify the costs of setting up a separate business. She makes pottery and only makes 2 or 3 sales per year with a profit of $50 and wants the ability to setup accounts with a wholesaler to buy clay using your company name. In other words what she really wants is to get some discounts on her hobby supplies by virtue of your company.
Finally while I am sure it is not applicable in your case, half the marriages in America end in divorce. What happens to the company if there is just one and your businesses are co-mingled?