There's no exact expression to use in this case, it is more a case of attitude and the way you say it.
You would say the sorry in a sarcastic or dismissive way which would show you don't really mean it. Also adding "whatever" to the expression gives it another level of disinterest. It's quite a common word and attitude, for teenagers especially, to adopt.
For the second example, again, the attitude is very important. You would add the "Happy now?" part in a very annoyed manner and frustrated manner.
As another anchor explained, this is more of a case of voice tone and attitude because you could simply just say "sorry" and leave it at that but if you don't want to seem rude you could say "sorry+(some excuse)" So if you came home late because you were just having fun with friends and you don't want to tell the truth completely then you could say something like " Sorry, I lost track of time."
Also the other example that I wrote "okay, okay. I'll be more careful." says okay twice because it's a way to tell them person to leave you alone... because deep down you might want to say "Leave me alone" but you don't want to sound rude or disrespectful so you say a simple "okay" plus "I'll be more careful(next time)" to avoid further questioning or conflict from that person.
別のアンカーが説明されているように、これは声のトーンと態度の問題です。
単に"sorry"（申し訳ありません）と言ってそのままにしておくことができますが、
失礼な態度をとりたくない場合はsorry+(some excuse)"（申し訳ありません+理由、言い訳）で謝ることができるでしょう。
だから、もしあなたが友達と楽しい時間を過ごして夜遅くに帰宅した場合、真実を完全に伝えたくない場合は、" Sorry, I lost track of time."（ごめんなさい、時間をすっかり忘れていました）の様に伝える事が出来るでしょう。
私が書いたもう一つの例は、"okay, okay. I'll be more careful."（わかりました、わかりました。もっと気をつけます）。Okayを二回文章内に使っています。これはその人に一人にしてほしい事を伝える言い方です。本当は "Leave me alone"（私を一人にしてください）と言いたいところかもしれませんが、失礼や無礼な言い方にしたくないので、その人からのそれ以上の質問や言い争いを避けるためにOkayに"I'll be more careful(next time)"（（次回）はもっと気を付けるよ）をつけ加えます。
2. Thanks for worrying about me. Sorry for bothering you.
3. Sorry for being a pain, but there's no need to worry!
These comments are positive ones. It is a parent' duty to worry about their children. It should not be difficult to apologise - even if you have done nothing wrong :-)
1. You apologise. You tell your parents nothing bad was intended.
2. You tell your parents you appreciate their concern - and apologise.
3. You apologise and tell your parents to try not to worry.
>No need to worry guys...
*This is an informal way and not expressing to much feelings.
..................
>Sorry, my bad.
*This shows that you do not really mean what you and that you are just saying it out of a little bit of respect.
.............**...........
No need to worry guys...
感情を表現せず、丁寧ではない表現です。
Sorry, my bad.
謝りたくないので、ただ軽く伝えるだけの表現です。
When dealing with your parents it is usually best not to be rude/sarcastic as it might cause more trouble and your parents job is to look after and worry about you, so even if you don't really mean it then it is best to say sorry anyway and you could add 'I didn't mean to worry you' or 'I'll be more careful next time' this would make the situation a lot calmer
親に対しては失礼な態度を取ったり皮肉を言ったりしない方がいいです。問題が余計に大きくなるかもしれませんし、子どもの面倒を見たり心配をすることは親の仕事ですから。なので、たとえ反省していなかったとしても、謝った方がいいです。そして、
'I didn't mean to worry you'（心配させるつもりはなかった）
または、
'I'll be more careful next time'（これからはもっと気をつける）
と加えられます。この方がずっと平和的です。
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