YANBU, I am Northern, and despite going to private school and university, I have never lost my northern twang ... and I have no intention to either! Yes it is a lot softer than it used to be, but that is more from the 10 years I spent abroad teaching English to children, so I learnt to speak slowly, clearly and enunciate properly for their educational benefit, not because I was actively trying to lose my accent. My flatmate always used to comment that he knew whenever I was calling home because my accent would come back really heavy and my speech would speed up tenfold 
As for your SIL, kill her with kindness and sweet passive agression ... if she calls you on it you can just act shocked that she has misunderstood you and she's the one who comes out looking bad, not you.
Both me and our two kids have Northern accents and despite having very soft accents, she continuously pretends she can't understand what we're saying or does impersonations of how we talk.
"Oh, SIL is that how you hear us speaking? That's nothing like how we speak, and since you've mentioned this before I'm concerned that you may have some issues with your hearing that is distorting our speech, I really think you need to see a doctor to check it's not serious." ... then if she does it again at further gatherings "Oh, SIL have you not been to see the doctor about that hearing issue yet, because you're still having the same issue and I'm concerned that it could be getting worse!"
"Your children need a haircut"
How kind of you to take an interest! It has been a while since their last cut, but they love their style and they're happy with it, why would we make them cut it?
"Their jeans are getting a bit short in the leg!"
Oh, yes they are, but these children will keep growing, it's so hard to keep up when their lives are so full of fulfilling and rewarding activities, who's got time to spend hours just shopping?
She is a raving snob and talks about football being "common" as she knows my elder son is football crazy. She'd rather go to "rugger!"
Yes, I suppose it is rather a common sport, being played in almost every country in the world but I'll just be happy as long as he's not an Aston Villa fan like Prince William or an Arsenal fan like Prince Harry, they're such common teams with such common fans, don't you think?