Two of (whom vs them), the twins pushes (one another vs each other).
SCRIPT
As she walks, her other three children, all little boys, two of whom are twins, walk in front of the stroller, the twins pushing each other as they walk.

QUESTION
#1. Which one is more suitable and what's the exact difference?
- two of them are twins vs two of whom are twins.

#2. Which one is more proper and what's the exact difference?
the twins pushing each other vs the twins pushing one anohter.

I believe you can help! Thank you sooo much!

Question

Two of (whom vs them), the twins pushes (one another vs each other).
SCRIPT
As she walks, her other three children, all little boys, two of whom are twins, walk in front of the stroller, the twins pushing each other as they walk.

QUESTION
#1. Which one is more suitable and what's the exact difference?
-> two of them are twins vs two of whom are twins.

#2. Which one is more proper and what's the exact difference?
the twins pushing each other vs the twins pushing one anohter.

I believe you can help! Thank you sooo much!

Answer

If i remember my grammar correctly, the sentence as originally written in your example is correct.

"'Two of whom are twins" is a relative clause, a subordinate clause that modifies the noun ''children."  "Two of them are twins" would be an complete sentence and would not be set apart by commas in the original sentence.

The grammatical rule is that "each other"'is used when referring to two people and "one another" when referring to three of more, although this rule seems to be ignored with regularity in the US.

Answer

All of them are correct but in each case the second example 'sounds' more correct. Also in the second sentence it can be taken in different contexts as in 'the twins pushing each other' implies they are both pushing or taking it in turns. 'twins pushing one another can mean just one is pushing or both are but not at the same time.