This is a difficult one. You know that losing weight would be great for your MIL and for you low carbing has worked. Your MIL has seen this and as already said you can not make someone change their lifestyle if they are not committed to it.

Just be there for her. Lead by example, but don't harp on about it. If she comes for meals do nice low carb meals and make her realise that there is good food on the low carb lifestyle. If she is stressed, then this is not a good time to diet for anyone as commitment levels are low and stress prevents weight loss.

Let her come round to her own decision on this. I know that if I am backed into a corner I will choose the opposite from what is expected, even if I know it is wrong!