Take responsibility for everything that happens to you and in your life. Take responsibility for everything that is in your control. However, feeling that you are responsible for others happiness and feeling that you did something when somebody is unhappy or in a bad mood because of their own attitude then it is as bad and as was complaining and blaming everyone and everything else in this world for your problems.
Taking responsibility for how others feel, accept life and their happiness is similar to complaining and blaming for what is going on in your life.
We are living a society where victim mentality is being revered. We are developing a society where adults and matured people who think rationally are scared by people who do not take any responsibility, who are complainers and constant naggers, who blame everything and everyone for their unhappiness and problems.
So there is a fine balance that we need to maintain even when we are taking responsibilities. We cannot take responsibility for what others do and their own decisions. Every person has to take their own decisions and need to learn to accept the consequences of their decisions.
Of course we cannot leave our close ones and not be supportive of them. But at the same time you must define some boundaries and need to involve your people to be responsible for their actions. You need to discuss and constantly remind them that you will help and support to your best, but the other person must think for themselves and be responsible for the choices they make.
*Do read the Disclaimer