Wow, you do have problems, the kids ages don't help either - problem years & years when they're testing anyway much less with all this going on.
Seems like some individual & family counselling or even support groups (for kids separate to you & your husband) as you all have a need to vent & say things that shouldn't be said in front of each other or the kids especially!! No point you doing the same as the ex. Talk (if possible) to the cousellors at the kids schools so that they're aware of what's going on & can be on the look out for behaviour changes & know to also let you know not just the ex.
Be there for each of the kids, separately & as a group - give them time & things (things aren't just expensive stuff) & let them know you'll listen but be firm -0 it sounds like thier mother wouldn't really do any of that especially not be firm or give her time - much less actually listen to them.
As to her putting on a good show in court - if a private investigator is out of the question cost wise - is there a friend the ex doesn't know who would follow & take some photos/video of her behaviour?? This may not seem right but where kids are concerned I don't care about right only what is best. I was a child welfare officer & a probation & parole officer so I do have some idea of what i'm talking about.