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I haven't been able to focus on painting nor update my art blog since I returned from America.

You need to match the tenses. Focus on painting = present so update should also be present. You could have written "I haven't been able to focus on painting, nor have I updated my art blog...."

For several days I had been suffering from a jet lag.

I prefer "When I arrived back in Japan, I suffered from jet lag for several days."

After I recovered (from it), I returned to my normal life as a wife, (a) mom and (an) English learner.

You can just say 'wife, mum and English learner' (note I use mum, rather than mom, being British)

I don't know why, but somehow, going back to being a painter is always the hardest thing for me after studying abroad.

I always can't paint for a while, every time.

Today, I was absent from my painting school because I didn't feel like that I wanted to paint.

I prefer "I didn't feel like painting". "Absent" seems a little formal here. Perhaps "did not go to" instead?

I had thought I wanted to paint this, that, it and so on all the time. I thought about painting all sorts of things all the time.

Your grammar is fine, but to me the English is not very natural. When we say "this and that" in the way that you do, it sounds as though we don't really want to give detail. For example: A says to B "What were you up to today?" B replies "Oh, this and that." In this case, this and that really means "nothing much" or "I don't really want to give a lot of detail about my day."

I really think my painting is affected by my feelings and my mood and is dependent on them.

I have to think a lot of things about: my daughter's future, my mom-in-law, myself and so on.

I have to take my first step because everything starts from it!

It's always difficult for me to begin painting again.

While I was in America, I had so many ideas for new painting projects.

I had visions of painting so many different things, one after the other.

My feelings and my moods determine my motivation to paint.

There are so many things on my mind now such as my daughter's future, my mother-in-law's health, and my own situation.

Painting is the thing on which I would really love to focus.

Everything starts with a first step and now is the time for me to take it.