which one is correct and why?

Question

could you wait a moment? i would like to stop............my mother
1-to telephone
2-telephoning

Answer 1

Could you wait a moment, please, I need to telephone my mother?

Number one is correct.
Notice I've edited your sentence. Why?
It makes more sense to connect the two sentences.
It establishes the cause and effect relationship implied by the two separate sentences.

You could say:
Could you wait a moment, I'm telephoning my mother.
This sentence means: I'm doing it NOW!

Could you wait a moment, please, I need to telephone my mother?
This sentence means: I want to do it; it refers to a future act.

So you use the expression which best carries the meaning you want to say.

Answer 2

My mother is on the other line.

or

My mother is due to telephone

according to circumstances. The first can be used if you have a system allowing someone to break into your call and the other can be used if you had an arrangement for your mother to telephone you at that time.

Answer 3

STOP TO __(INF) = I want to quit doing what I'm doing, so that I can do something else

STOP ___-ING = I want to quit doing something

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Imagine if you're driving a car with a friend. She says to you,
"I would like to stop to telephone my mother". This means she wants you to pull over to the side of the road, to the nearest telephone, so she can call her mother.

If she said, "I want to stop telephoning my mother", it means she doesn't want to call her mother on the phone anymore.

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NB: Native speakers rarely use "telephone" as a verb. Use "ring" (UK) or "call" (US) instead.

Answer 4

both are wrong . you should never try to stop any sort of communication with your MOTHER at any time and under any circumstances.