Subject + "have had" + bare infinitive ... ever correct?

In writing an email today I came up with the following sentence:

"We have had two other ladies express an interest in the room."

I'm a native English-English speaker and this felt fine to me. My partner (who is Spanish) felt that the bare-infinitive 'express' in conjunction with the 'have had' was wrong. She felt the closest acceptable option would be the gerund form ie:

"We have had two other ladies expressing an interest in the room."

To me that sounds less normal and a slightly different meaning.

It is something to do with the 'had' specifically, because she felt (as I do) that with a different verb it could be correct, eg:

"We have heard two other ladies express an interest in the room."

I searched online for grammar reference sites and the closest I could find to an example matching my construction was specific to having someone do something for you, for example:

"I have had my lawyer look into it"

(and it was noted that this was an American English construction)

But is this valid in my case?

I'd like someone to confirm or refute whether my original phrase is correct, preferably with an external reference :)

In the original sentence,

We have had two other ladies express an interest in the room.

the perfect construction, and the nature of the particular noun phrases and complement in the sentence are all irrelevant to the grammar. Let's start with a simple sentence without all the bells and whistles and see what's what.

There is an idiom with have plus either an infinitive complement or a gerund complement. It means to cause someone to do something, which is described in the complement.

• They had us look for her earrings.
• They had us looking for her earrings.

This is not, by the way, a "bare infinitive" (or gerund) -- it doesn't use to, true, but it has to have a subject (us in the examples above). Without a subject, neither is grammatical.

• *They had look for her earrings.
• *They had looking for her earrings.

Nonagentive sense verbs (see, hear, feel, smell, taste) also work like this have construction -- they can occur without a to complementizer for an infinitive, and they can also occur with a gerund, both of which need subjects (I saw him run/running past, I heard him practice/practicing the flute -- but you can't delete him).

There's no problem with any of the sentences you propose. Actually, I find "We have had two other ladies expressing an interest in the room." to be less natural than your alternative. (I don't know how to look up any evidence though.)