About the coupling of ーてもらう and ーなさい

Question

I often hear my old calligraphy teacher (and so far only her) use something like the following:

何々。。。書いてもらいなさい（？）

何々。。。やってもらいなさい（？）

and so on. The question mark in parenthesis indicates that, if I hear the intonation correctly, it seems more like a kind request rather than an imperative. Or at least, kind of in between a request and an order, exactly as the the two forms suggest.

The meaning is quite obvious, I am mostly interested in the following.

Nuances.

How does this differ from simply using ーてもらえる？　ーてくれる？ or the ーなさい forms alone?

Speech style.

Is it something somewhat old fashioned? I'm asking just because as I mentioned above so far I have only ever heard this from an old lady.

Actual meaning

I find it quite difficult to give a literal translation. Somehow, ーてもらえる? and ーなさい seem almost opposites to me (one a request, one an order). Am I correct in interpreting this as "please do this?", or is there a better way of putting this?

If possible, I would also appreciate a few extra examples of usage.

EDIT:

Reading and thinking on a comment by @By137 I wonder if I misheard all this time and wasn't actually 。。。て御覧{ごらん}なさい. Obviously rather than my poor listening skills I'll say that this is due to my old teacher being very old and speaking in very incomprehensible way... which is false. I'll ask myself next time and eventually edit or close the question, although it could still be a good question for the てもらいなさい form.

Answer 1

~てくれる? Is a (casual) request, but it lacks demand. Which is why it's in a question format. ~てもらいなさい is a demand used when talking to someone of lower status then you. You can hear なさい when parents order their kids to do something. She adds the questioning tone to not have a sense of reprimanding.