The verb have can be followed by object + infinitive / -ing form. This structure can have two meanings: ‘to cause to happen’ or ‘to experience’. Note that in this case, the infinitive and the –ing form can be used with little or no difference in meaning.
He had me wash his car. OR He had me washing his car.
The teacher had the boy recite the poem. OR The teacher had the boy reciting the poem.
The infinitive form is preferred when we are talking about things that happen, have already happened or might happen in the future.
We have never had customers complain about the quality of our products. (It never happened to us. Our customers have never complained about the quality of our products. )
She has never had people misbehave with her.
Here we use the infinitive form because people have never misbehaved with her.
We use the –ing form when we are talking about things that are happening, were happening or might be happening. As you know, continuous tenses are used to talk about situations in progress.
Her performance was simply superb. She had us literally crying with joy. (= We were laughing.)
Now that the winter is over, it is lovely to have kids playing in the garden again. (= The kids are playing in the garden.)
I opened the storeroom and found that we had mice running around the cabinets. (= The mice were running around the cabinets.)
I won’t have…
The expression I won’t have is used to mean I won’t allow. In this case, we prefer an –ing form.
I won’t have you smoking in my presence. (= I won’t allow you to smoke in my presence.)
She won’t have him telling her what she should do. (= She won’t allow him to tell her what she should do.)