R. Kelly's Ex-Wife I Have No Problem w/ His $22k Gig ... He's Got Responsibilitie$$$

EXCLUSIVE

imageR. Kelly[1] going to a club for an hour and walking away with $22k cash might have lots of people upset -- but his ex-wife sure ain't one of them ... quite the opposite, actually.

A rep for Drea Kelly -- R. Kelly's ex of more than 10 years -- tells TMZ ... she takes no issue with R. Kelly getting out there and making a buck -- but not because she thinks he's innocent ... it's more about what it means for her and their kids.

We broke the story ... R. Kelly showed up to a club[2] in Springfield, Illinois over the weekend, where he sang a bit of "Bump N' Grind," hung out for less than an hour ... and walked away with $22,000[3]. He asked the media to go easy on him[4], as this was just a means to an end.

We're told Drea sees it this way ... if R. Kelly's working to fulfill his financial obligations[5], "no one can be mad at him for that." Besides, Drea's rep tells us the man certainly has responsibilities that need tending to with dough ... for the sake of his kids.

As we reported ... R. Kelly went BACK to jail[6] last month because he couldn't pony up his back child support bill[7] ... more than $160k. He got sent to the can but was bailed out[8] when someone covered his tab after spotting him (again

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