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Here's a context.

Sales team is thinking of expanding their business in Chinese market, but one of their members, who speaks fluent Chinese, has been assigned to work in the marketing department. So the team leader is really worried that it could become a serious problem doing business in Chinese markets.

And now, as a person in personnel, I'd like to do something for them. So,

Seeing that you are in trouble doing business in Chinese market, we need to do something for you. After checking into the situation, we've decided to let him with you.

Here is it possible that I write doing business in Chinese market right after trouble in the same way that we do in this sentence: We have a trouble doing our business in China.

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The meaning of the phrase in trouble:

1) in danger; in difficulty; due for punishment.
2) Euph. pregnant and unmarried

is different than trouble, which generally means difficulty or distress.

In your example, you mean that you are having difficulty doing business, but you are not in danger or under threat of punishment (I hope). Therefore you should use having trouble:

Seeing that you are having trouble doing business in the Chinese market, we need to do something for you. After checking into the situation, we've decided to let him with you.

In the definitions, one for in trouble is "in difficulty" but this more refers to a specific personal impact, not to a transactional situation.

BTW, let is not used properly, I can't tell for sure but maybe you mean leave?

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In my view to have trouble doing sth is a verbal idiom with gerund derived from: to have trouble with doing something. It is a mere convention that the community has adopted the gerund as complement instead of the to-infinitive which theoretically would do as well.

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Yes it is possible to use your second sentences but with some changes to:

We are having trouble doing our business in China.

That is because trouble isn't something you can count.

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