It should be, I believe "She is having difficulty shopping." But I am not sure how I can explain to someone who is a non-native English speaker why the form "She is having difficulty to shop" is not correct but "She is having difficulty shopping" is okay.
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4This belongs on English Language Learner's SE. You may find that site more useful. // Also +1 tchrist – hunter2 Jul 29 '13 at 03:24
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3What is wrong is that the predicate have difficulty can take an Equi gerund complement, but not an Equi infinitive complement. – John Lawler Jul 29 '13 at 03:31
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1after an adjective, verbs will (very) often take the gerund (ing) form. E.g It's not easy studying a new language. – Mari-Lou A Jul 29 '13 at 07:52
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This question appears to be off-topic because it belongs on [ell.se] – TrevorD Jul 29 '13 at 11:10