Is it legal for a company to offer a different insurance rate based on the spouse's employer's offerings?
Given the scenario you describe, your employer is not charging you a different rate if your spouse is eligible for insurance from your spouse's employer.
Under the Affordable Care Act, when an employer decides to provide health coverage to their employees there is no requirement to provide insurance to the employee's spouse.
Extending coverage to an employee's spouse carries additional cost to the employer. Many employers implement surcharges for those employee's spouses if coverage is otherwise available to the spouse. Essentially, when coverage is available to a spouse through their employer and they choose to be covered by their spouse's employer they are making a choice, one would presume, for better coverage. In this case, the employer is seeking to recover some of their cost for covering someone who would otherwise have coverage.
From this article dated January, 2014, you can see that many employers are moving in this direction. That article references an article regarding UPS. UPS is excluding any spouses from coverage if they would otherwise have coverage from elsewhere.
You ask what right do they have to this information [that your spouse has coverage available elsewhere]?
You are asking your employer to extend health coverage to your spouse, a benefit that your employer apparently provides. Your employer has the right to ask you information regarding that benefit extension you have requested. If you don't have a spouse or you aren't seeking to have your employer increase their benefit cost by extending coverage to your spouse then there is no reason for them to know if your spouse is covered.
What other legal means do they have to find out this information?
They should only be seeking this information because you've decided to ask them to provide a benefit to your spouse. If you were to lie about this information then they would have the same facilities available for any other fraudulent act to gain a benefit contrary to the employer's policy.
Does this constitute illegal discrimination?
Based on what? The employer is not required to extend the benefit to your spouse. The employer's policy for extending that benefit is to charge $50 for any spouse who could otherwise be covered by their employer. If you want the benefit then answer the question truthfully and, if your spouse is otherwise eligible for coverage, then pay the $50. If you don't want to answer the question then don't request the benefit.
I am aware of similar policies regarding smoking which are similarly controversial. What conclusions can we draw from that precedent?
What precedent, that it is legal to charge smokers more for health insurance? The Affordable Care Act allows insurance providers to charge up to 50% higher premiums for smokers.
Here's an article from the Society for Human Resource Management:
Most employers using a spousal surcharge require an employee who enrolls a spouse in the plan to pay the surcharge unless the employee can verify that the spouse is not eligible to enroll in his or her plan, is eligible but not allowed to participate for a particular reason, or is not employed.