HAVE, GET + object + present participle

Have/get + object + present participle can mean "persuade someone to do something":

The teacher had the whole class singing Mary Had a Little Lamb.
The boss got the staff working overtime.

It can also mean "experience something happening to you as a result of something":

We'll have my brother staying with us for a little while until he finds a new apartment.
His problems got him going to hospital for years.

Here, the present participle expresses repeated action, or something happening over a period of time.