Are they both grammatical? <Someone> will have you take a bath

Question

I was watching a Japanese anime on Youtube, and came across this line of subtitle text:

We will have you take a bath.

I could not fully understand its meaning, but I guessed it was some kind of command. I have searched on Google, and found some similar words: (Juvenile Fiction)

(“And since you mentioned a pot of boiling water, I think I will have you take a bath before your operation...)

What is this kind of grammar? Why the verbs, take are not in past tense in the two given sentences.

If I change the verbs in past tense:

We will have you taken a bath.

I think I will have you taken a bath before operation.

Are they both grammatical?

Answer 1

The "I will have you (do something)" is a mild imperative, similar to "I'm telling you (to) (do something)" or "I require you (to) (do something)" but a little more polite. I believe the grammar is "to have (someone)" + infinitive. Some examples:

I'll have you know that I am not left-handed.

We'll have you check in your cell phone before the examination.

I'll have you fill out these forms before I process your application.

The "have" part can be any tense that makes sense in the context, but the following verb is not conjugated.

They had her take a drug test before she was hired.

We used to have the team run around the field ten times before practice, but now we just have them run once around the entire school.

They've had her ride her bicycle to school every day this week.

Note that this form is not a request. It is meant to be a command, but phrased in such a way that it sounds more like a request, and therefore is more friendly. See for example, the contrast between these two demands:

Get off of that table!

I'll have you get off that table, please.

Answer 2

Neither are grammatical. To answer your second question as to the kind of grammar, these are called "causative verbs."

It sounds to me like the "have" is confusing you. In this case, "have" is not indicating anything having to do with when something was done (eg. "I have paid the bill" indicates that one has paid a bill in the past). Instead, "have" is meant to convey that the person will "have to" (be required or asked) to take a bath.