I don't understand why the tenants are not claiming housing benefit; surely if they do, and get it paid to the OP, the problems will all be resolved and noone will need to be made homeless.
As dreaming has said, there is a baby involved here, that realistically WILL HAVE NO HOME TO GO TO. That may be the tenants' fault as much as the landlady's, however at the end of the day, I stick by my point that renting a home is NOT the same as selling any other (non-essential) commodity. This family will not have the option of just moving in somewhere else if made homeless from here. If they can't afford the rent now, where are they going to get 1-2 months rent as deposit, plus another months rent uppfront, plus fees from? And I daresay this landlord's great reference will make it that much easier.
The fact is that this baby did not ask to be born and does not deserve to be born in a gutter, no matter how irresponsible its parents may or may not be (NOTE: we've not heard their side of the story at all; there may be a v good reason why they haven't paid the rent that is not their fault; the landlord may not be telling the full story here).
I repeat - if you become a landlord, your responsibilities are not just about collecting the rent and paying it into your bank account, as some people seem to think. You are providing someone's HOME. That matters, beyond a financial level. If you don't like this, make money in less emotive ways, providing a less essential service.
maxybrown's attempts at analogy left me cold - not really clear what she was getting at. A better analogy would be the health service - in this country, because it is a civilised one, our hospitals will help anyone sick who comes to them in urgent need of medical assistance, and worry about the bill later. In the US, they won't treat you until they've seen your insurance certificate. Some people may argue that's fine and as it should be. I would argue that is fundamentally inhumane.
And no, well-researched arguments such as calling me an 'idiot'
won't make change my mind on this.
OP. Your husband is right, and you should be proud of having married such a caring guy. Or 'idiot', as others would see it. 