In the morning I wake up late, around 9.30am and the awakening was beautiful because was my daughter who woke me up with a kiss.

To make it feel more natural you could say “ I woke up late this morning, around 9:30am, by the beautiful daughter who gave me a kiss”

ILater in the afternoon, I accompanied my son to the pool, because Hhe receives swimming classes.

Right now, its the night time in my city, and the rest of afternoon was quite quiet.

In the morning I waoke up late, around 9.:30am, and the awakening was beautiful because was my daughter who woke me up with a kiss.

More natural: "I woke up late this morning, around 9:30am. Waking up was beautiful, because my daughter woke me up with a kiss."

In the afternoon, I accompanied my son to the pool, because Hhe receives swimming classes.

More natural,
"In the afternoon, I went with my son to the pool for his swimming lessons."

Right now, is thet's night in my city, and the rest of afternoon was quite quiet.

In the morning I waoke up late, around 9.30am and the awakening. Waking up was beautiful because was my daughter who woke me up with a kiss.

In the afternoon I accompanied my son to the pool, because Hhe receivesis taking swimming classes.

When we went back home, my daughter fell asleep and my son stayed so quiet.

“When we returned home…” would also work well.

Right now, is the night in my city, and the rest of afternoon was quite quiet.The rest of afternoon was quite quiet and it’s now nighttime in my city.

It’s clearer to have the order of events chronological.