Watching Videos about Volcanoes

If you're talking about some volcanoes in general, use "Volcanoes".
If you're talking about a specific volcano, use the actual name of the volcano.

I watched a YouTube video about volcanoes with my kids.

Because tThere was a big submarine volcano in Japan, so we watched YouTubea video about it.

You have already mentioned "YouTube" in the previous sentence, so I don't think we need to repeat it. You can just use "video".

Also, use only one of "because" or "so". You shouldn't use both in the same sentence.

With the help of the videos, I hope they can understand it.

Actually, I made a plan to travel to Japan few years ago for watchingto see a volcano mountain.

To express a purpose, use "to" + infinitive form of the verb. (Not "for" + verb-ING). This is called 'the infinitive of purpose'.
E.g. I run to catch the train in time.
I eat vegetables to stay healthy.
I go on holiday to relax.

I think, experiencing being on the mountain is the best for my kids, so I was trying the way to go there.

If we put "I think" at the start of the sentence, it doesn't need a comma (,) before explaining the thing you think.

After the restriction will be endeds, we will travel to Japan.

We can't use the word "after" with "will" in the same clause.
We use the present simple ("ends") for scheduled events - things we are (fairly) certain will happen or that are planned.