Help to clearly understand 'TO' when object becomes new subject

Question

Some dictionaries seem to indicate that 'TO' in some sentences is just there to 'mark the infinitive', thus giving meaning to the sentence

and they list examples like these:

I want TO open the window
I want her TO open the door

but that can't be it... the same definition of 'TO' for all sentences. Especially since I see two people involved in the second sentence, and that seems to be enough to call them 'different'. Two people, two actions, how are they really affected by that 'TO'? What role do they exactly play in the sentence, grammatically speaking?

In sentences such as the following:

I want her TO open the window
I need him TO give me money
I asked them TO leave the room
I ordered them TO shut up

Are the objects(people) to be the doers of the second action(infinitives) i.e:
she will open the window
he will give me money
they will leave the room
they will shut up

and that that is what I want/need/asked/ordered?

Answer 1

You've already noticed the difference between your two example sentences:

I want to open the window - no noun or pronoun between "want" and "to open."

But

I want her to open the door - there is a noun or pronoun between "want" and "to open."

The difference isn't how the word "to" functions. The difference is whether a direct or indirect object comes between the main verb ("want") and the infinitive ("to open").

When there is no noun or pronoun between the verb and the infinitive, the subject of the main verb is the actor or agent of the infinitive.

Where there is a noun or pronoun (acting as direct or indirect object of the verb) between the verb and the infinitive, then that noun or pronoun is the actor or agent of the infinitive.

Some verbs can only be followed directly by the infinitive. Some verbs can only be followed by an object + the infinitive. And some can use either construction.

Answer 2

The verb construction verb + noun (accusative) + to-infinitive was one of the favourite constructions in Latin called aci, accusative cum (with) infinitive.

The traditional view of the construction "I want her to open the window" is that "I want" is followed by a two-part object, consisting of a noun/pronoun + to-infinitive. The noun, a direct object to "want", is logical subject of "her to open the window". You can transform the sentence to "I want that she opens the window".

The "to" is the normal "to" that marks an infinitive.

As to the derivation of such a special construction my guess is "I want from you the opening of the window". A to-infinitive is related to a noun-form and "from" was dropped in the course of time.

In other cases the noun was orginally a dative (indirect object) as in "I ordered him to go" that may be understood as "I ordered him the going".

If you need a name for this verb construction I call it ati-construction, accusative + to-infinitive. In English grammars you won't find this term.