Lucy you and I must agree to differ there. I am very pro no-kill policies although I agree with you that the Rottie you met deserved a chance, as did you, as you know your Rottie "stuff".
One of those in my local rescue is there for life - he is a GSD, and not suitable for rehoming, a soppy date with the rescue owner but not to be trusted with others (you just can't get near him, he has no trust with and reacts very badly to strangers).
However in the rescue he has love, warmth, food, play, exercise, the copanionship of the rescue owner and canine friends (something which is a shock to us all, it took time to get him to trust other dogs too). Perhaps he's lucky that this is an independent, small rescue, where they have more time and commitment than the DT? I don't know... I'm just glad he is still alive, albeit that he will never be on a sofa in a house as my 2 dogs are tonight.
Paddling, as you've gathered, I'm very pro dog, but I still maintain that until your MIL has got on top of this issue YANBU in saying that the dog isn't welcome - MIL can put in a routine and training programme and the Rottie will hopefully find her place in the home, her safe space to escape family life and discover that there is no need to bare teeth to safeguard herself (as my own previously abused dog has here with me and my DC). To come to your house where everything, rooms, safe space, people, rules, are different, is clearly not an option.