I'm sorry you are in this horrible situation.
I want to address just one key part of it, since others have addressed much of it.
Your husband is not, as someone else put it, on the same page with you. I assume you mean he is doing nothing about the situation and does not have any intention of sittiing everyone down and saying either "We are evicting you" (IF you have that legal right -- I'm not clear on whose names are on this mortgage) or saying "You must pay us X amount in rent or...we are evicting you" or anything else.
You need your husband on your side -- the side of actually taking an action, rather than letting this living arrangement go on and on and on. Here's an idea: If your husband won't listen to YOU about this, do you think he might actually wake up and listen if a third party tells him what a stupid deal he's making with this living situation? Some people won't listen to close family or friends, but WILL sit up and pay attention if a professional tells them the same things.
Go to your bank. Set up an appointment with a financial adviser there, someone with knowledge of real estate and taxes. Banks provide this for free! Go in yourself the first time, lay out the situation but be unemotional and don't badmouth anyone; just term it as "We want to know what risks we are running here." Be sure to bring all the documents -- the mortgage; any written agreements (have there been any? If not, you are not protecting yourselves!) between your family and the SIL/BIL regarding rents etc; the documents for the $35,000 loan your family took out to cover their family's taxes; everything. Then at a second meeting, you AND your husband sit down and ask the financial adviser: What are our risks here? How do we get ourselves out of this situation?
I think any good financial adviser is going to tell you that your whole family is at big financial risk here in several ways -- ownership of the house (still not clear to me if it's your family's or jointly owned with the other family), the fact you now owe a large loan on debt someone else incurred, etc. Find out what your risks are and have the adviser make clear to your husband what the consequences will be to YOUR family if the other family continues this lifestyle: You could lose the house completely if you can't afford the mortgage due to SIL/BIL's refusal to pay rent; you could lose it if your repayment of the loan falls behind; there could be tax issues involved in your paying off someone else's taxes; and much more.
Your husband needs to understand that this situation puts his children's futures at risk; could take the roof from over your heads; could jeopardize any college fund you hope to save for your kids; and could put you in legal or tax troubles as well. You are far too entangled legally and financially with these relatives.
If he hears it from a professional at a bank sitting in an office, he may finally wake up. This may all end up even with the adviser sitting down with all of you, including SIL and BIL, if they are willing to work out a payment plan etc.
The important thing is getting your husband to come around and realize that, though he may think "They're family, we'll just carry them," he is putting his kids' home and future at huge risk. Time to stop. If you can make it all about "This is what the bank guy says," rather than, "We're sick of your taking advantage of us," it may also be easier to tell the SIL/BIL they must shape up or ship out -- you can put it on what the professional is advising you, rather than having it be so emotional and personal.