I am a good-natured person. I am strict with neither students nor my own children. I had thought my approach to be all right. However, when recently one student was inattentive during my English lessons, her mother asked me to be stricter. I never heed people I know to be wrong, but this time I considered her request to have some merit. I decided to try to change my approach with my students as well as with my own kids. For example, I usually pamper my daughter and my praise for her is unconditional. But, realistically, I know that no one can be perfect. So yesterday, after she had played and procastinated until late without doing her homework, I scolded her. She resented this at first, but later came to realize it to be her mistake after all. I hope in the future to strike a balance between loving and teaching the children well.
A parent cannot "tell" you to be stricter. They are not your boss. They can only "ask" or "request" that you be stricter.
It is not important, but I prefer "I decided to change" to "I decided changing". Use participles to create images. Use infinitives to state precise facts. Here you are simply stating a fact.
You think "well" of someone, not "good". "Good" is an adjective, so it cannot modify "think". You can however think "good thoughts" about someone, because that way "good" modifies the noun "thoughts", not the verb "think".
"Kids" is a good word, but don't overuse it. "Children" is the more formal word.
"So yesterday", not "but yesterday". "But" is used to state something contrary, but there is nothing contrary here.