call someone vs. call to someone

Question

One sense of the verb "call" is "to shout loudly." I'd like to know whether the preposition "to" is optional in the following sentences:

Sheila was just sneaking out when her mother called (to) her.

She called out (to) her father for help.

Answer 1

Sheila was just sneaking out when her mother called to her. "Darling, don't forget the umbrella."

It means the mother shouted these words to her in order to get her attention. It implies they are at a distance from each other and a higher pitch might be necessary to deliver a message.

Sheila was just sneaking out when her mother called her. ["Sheila! Could you come over here?"]

It means she asked her daughter to come to her.

She called out to her father for help.

It means she shouted something to her father to get his attention (and, consequently, his help).

She called out her father for help.

I am not sure if it works this way. When used transitively, call out takes an object - something you can actually shout (a word, a name, a warning, a reprimand).

She called out her father name. She called out "Help!" to him.

If the father hadn't helped her, she might have called him out on it.