"have trouble doing" is correct and usable in written English.
You can use it when you want to express difficulty in completing an action or task. For example, "I have trouble doing math equations."
Too many doctors have trouble doing that.
We have trouble doing that".
If they have trouble doing that, they should look for work elsewhere".
It was clear from the early rounds, though, that Hatton would have trouble doing that.
And prescription-assistance programs, which are a tremendous amount of paperwork, which people have trouble doing.
Some people who have autism cannot live on their own, as they have trouble doing simple tasks, while other like myself have trouble doing very specific things, but can be comfortable working or studying.
Ordinary people would have trouble doing everyday things like shopping for themselves or paying bills, Dr. Fillit said.
When I know a particular child, for whatever reason — temperament, exhaustion, hunger, reluctance — is going to have trouble doing something that needs to be done.
She can beat someone senseless while talking about her feelings, something that traditional male action heroes on TV still have trouble doing in more than monosyllables.
"He had the ability to tell us what the car is doing on this part of the track, and some drivers have trouble doing that.
Human babies, by comparison, are lumps of flesh and bone that have trouble doing anything for themselves, including regulating their own temperature.
