Well uh... you can pretend she's a relative, one you tolerate more from because of family ties. Or you can choose to just not spend more time with her, even if it means you see him less. Is them them moving in together in some situation that means seeing him there involves her being around all the time?
I haven't spent time with somebody like that for decades, I'd never do so again. I've never had respect for somebody "grow on me" with time, people seem to learn to tolerate metamours if they don't get along, or stop spending time around them. I've never seen anybody say "I disliked my metamour but after 5 years of making myself spend my weekends listening to their idiocy I didn't notice it anymore!" I bet the best way you could learn to respect her, is remove her from your life conversationally so you stop getting reminded she is a chronic liar, and can enjoy the other positives about her from afar.
Happiness will never come to those who fail to appreciate what they already have.