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Uma Thurman is stuck between a rock and a hard place ... if she shoots a movie she won't see her daughter. That's the predicament she's in, thanks to her baby daddy.

Uma's ex-fiance, Arpad Busson, just filed legal docs asking a judge to prohibit her from taking their 4-year-old daughter to Europe while she shoots a movie ... sources familiar with the situation tell TMZ.
We're told Uma has been blindsided by the latest conflict ... she's supposed to leave in 2 days.
Arpad wants the kid to stay put in NYC, so now a judge will decide ... possibly creating a real-life "Sophie's Choice" for Uma.
TMZ broke the story ... Uma and Arpad's nasty custody battle heads to court in a few months to hash out visitation rights.
A rep for Uma tells us ... they'll let the lawyers and judge handle it.

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