You say the rent on sils home (mils old home) is £50 more than where she lived before, which would mean your rent reduced by £50, how on earth did your husband not spot the error when he reduced his standing order?
So for eg, sil was paying 300 a month, but her rent is now £350 after the swap
And you were paying £350 a month but it's now £300 after the swap.
If your dh didn't realise his error when he adjusted the direct debit to £300, and mil also didn't know her rent wasn't being paid, is it so unreasonable that the sil didn't know either?
Sil knew to stop paying on her old property, but did she actually pay anything on the new property? How can she be in arrears on the new one if you have been paying it? Or has she just not been paying the £50 extra?
It's staggering that the arears have been allowed to build up for six months, and part of me wonders if the reason your mil hasn't mentioned it before is because she knew sil wasn't actually paying what she should be on the new property?
I'd be annoyed too, with dh for not paying attention when adjusting the standing order, if it's been a case of sil has been paying council her rent and won't have been told she's in credit. (You'll need to chase the council if this is what's happened)
With sil if she's been aware and stuck her head in sand, she will say though that she's paying her own rent, plus the arrears and can't afford to pay you back.
And also with mil if it comes to light she knew sil was deliberately letting you and dh pay her rent but didn't speak up. This sounds more believable that the council letting two households run up arrears for six months to be honest.