I'm not so sure about that, gillstone.
First of all, they certainly could deny you a 1-bedroom apartment if you had, say, fifteen children. It would be child endangerment or negligence. So then the question becomes, at what point do children need their own room? 12 children? 8? 4? 2? 1? You have to draw the line somewhere. I'm sure the law *does* draw the line somewhere. It may in fact draw the line at 2 persons per bedroom, adults and children combined. We don't know without seeing the law.
Secondly, even though it's true that federal law trumps state law, a Fair Housing or HUD complaint is only going to hurt the landlord, not help the renter. If, in fact, there was an illegal discrimination, that will get the landlord in trouble once the complaint works its way through the system (which could take months), but it will not help the renter get the apartment... they would have to sue the landlord directly on the basis of that discrimination (not just file a complaint), and then after the court says its peace perhaps the landlord will be forced to revise their policy/procedure to come into compliance with federal law but that too can take months or longer, and the renter will have to find some other housing accomodation in the meantime.
Thirdly, a state law that says "2 persons per bedroom" that doesn't specify any attributes of the persons/human beings, is not discriminatory. You can't discriminate based on unknown information. If the law is based on the number of human beings, and the law is applied equally to adults and children, I can see how that would not be discriminatory. You may disagree -- that would have to be adjudicated by a court.
Fourthly, there comes a point where it is not worth pursuing something even if you are right. You don't want to be in an adversarial / antagonistic relationship with your landlord, or anyone with whom you have a business relationship. It just pays to keep things amicable. Depending on the landlord's stance on this subject, it may be a situation where they don't actually care but just think they are upholding the law (and they could be mistaken), or it may be a situation where they have personal reasons for this policy and "state law" is an excuse that lets them implement it. In the latter case, if they cared about this particular rule for whatever reason (maybe they feel higher occupancy leads to more damage / maintenance expense), then trying to force your way in to residency may not be in your best interest. I don't see how getting a court order to allow you to live there is likely to be conducive to a pleasant living arrangement, no matter the length of the lease.
Here's what I would do:
1. Find out what the actual law is in your state, and county, and city, and what federal law says on the matter, so you are aware of the actual law in all 4 jurisdictions.
2. If you think the law allows you to live there, try to convince the landlord of their mistaken interpretation, but don't force the issue. If you're easily able to convince them, great -- otherwise move on. Maybe the next building that tries to pull the same thing on you will be more convincable if you have the facts about the law right at the start.
3. At the very least, you can use this topic as an initial question / discussion to filter down the prospective residences so you will waste less time investigating the ones that are unlikely to budge on this matter.
4. Your first priority is to yourself and your family, so find a place to live first. After that is all settled, if you feel your investigation has revealed that one or more landlords are engaging in practices that are contrary to the law, at this point you can file a complaint about them with HUD or other agencies.
That's just my opinion about what I would do -- I am not a lawyer and this is not legal advice! If you feel in the slightest bit uncomfortable dealing with this issue, maybe you should retain an attorney to get professional advice on the matter.