Not for AGES! According to most media outlets, it appears the marriage is over - he's been photographed intimately kissing another woman and Caroline has moved back to Monaco some time ago - but neither she nor Ernst August are publicly confirming or denying this and they are not obliged to, really, are they?
As to Caroline getting on or not getting on with Charlene, it was inevitable the press would invent stories that she doesn't, regardless of the truth. If Caroline's past interviews are to be believed, she claimed she'd be happy and grateful when Albert married as it would relieve her of many obligations she would rather not be involved with.