grammar - Can one say "A decides that B will do X" with ことにする?

Can one use ことにする to express the idea "A decides that B will do X"?

Take the sentence 私は外へ出ることにした. The way I see it, 私 is the subject of both 出る and した, with one usage omitted due to being understood. So in full the sentence is

私は｛私が外へ出る｝ことにした。
I decided to go outside.

Now what happens if the subjects are different? Can we say

AはBが外へ出ることにした。

A decided that B would go outside.

If this construction is not allowed, how else could you say this?

Answer

I think one of your assumptions is wrong. A nominalized verb phrase doesn't necessarily need a subject (omitted or otherwise). Take a look at the following sentence:

[ 嘘をつくこと ] は良くない。
[ Telling a lie ] is not good.

I don't think there's a recoverable subject in the verb phrase 嘘をつく. I think it's more like "telling a lie" or "to tell a lie" than "[someone] tells a lie". And I think the same thing is true about your example:

私は [ 外に出ること ] にした
^{As-for me, [ going outside ] decided-to}
= I decided [ to go outside ].

The nominalized verb phrase [ 外に出ること ] talks about the idea of going outside, but it doesn't specify an actor via a subject or anything else. There's no subject to recover here.

The topic 私 connects to the matrix verb した, not the embedded verb 出る. Usually a topic splits things into two parts:

私は　｜ 外に出ることにした
^topicは ｜ ^comment

This is called a topic-comment structure: the comment on the right tells us something about the topic on the left. Essentially, the topic connects with the entire verb phrase on the right half, the head of which is した. And that's why it can't connect with 出る, which is stuck inside a relative clause.

If you'd like to say you decided to make someone go outside, you can do so by getting rid of the intransitive 出る and putting the transitive (causative) 出す in its place (as jovanni suggested in this comment). This makes an を-role available inside the nominalized verb phrase:

私は [ snailboatを外に出すこと ] にした
^{As-for me, [ making snailboat go outside ] decided-to}
= I decided [ to make snailboat go outside ].

But you can't directly say "A decided that B will do X", only "A decided to make B do X". The ことにする idiom doesn't have a separate role for B to fill.

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(Note: in the above, ^decided-to really corresponds in meaning to ことにした, not just にした. Even though ことにする isn't a single constituent, it is a single idiom, so you can't really divide it up when talking about what it means.)