Totally agree.
That may not mean a heck of alot - people can 'own' things on credit they can't afford. Sometimes its more show than go. Of course if everything was done up and up, what was that credit based on...? or is it leased? (no answer needed - just pointing out both sides of the question)
Looking like cash was available... to say nothing of the parenting. Kids know..
...
This is the really tough part for you and your family. Both you and your wife know a big drama blowout won't solve anything - and can make your own home unpleasant. Keeping it in and doing nothing doesn't solve anything and is going to eat away at you, and does nothing for the kids. (plus your wife probly still cares about her sis)
Hoppy's suggestion is one route. If you and yours can figure out a non-drama strategy, it probably won't be a one shot, but a chipping away. Think about what the end results will look like; the ones you want, the ones that might happen, and the ones they may want. The last is important because if they they are going to be a part of it, they got to be motivated. Otherwise you're only strategy is going to be along the lines of what Hoppy said.