Holikimura it does sound like you perhaps did go back too soon. Although it wasn't as bad as you thought at first, the stress and anxiety surrounding the demands of your job have built up and now you feel overwhelmed. You have identified that work is not the best place for you to be, you would rather be at home and you feel like running away. These are very difficult feelings to have whilst trying to stay calm and productive in such an important job.
It is very important that you do explain your feelings to your line manager and in turn your head of school. It matters not one jot how much time you have had off before, or how disgruntled the head may or may not be. What is important is that you receive the support you need. If you need time off you must take it and you are within your right to do so. It is a difficult thing to personally process that you can not at the moment do something you know you are capable of and indeed once enjoyed, but the answer is that you are simply not capable of functioning in the same way at the moment and that is absolutely no fault of your own. What you are in control of however, is giving yourself the best possible chance of recovery by identifying what will aid it the best and allowing yourself those things. At the moment it is difficult to imagine being able or wanting to go back after the time off, but that is only because of how you are feeling at the moment. You will, with sufficient time off, start to realise that you feel you can and even would like to return, and only then will it be right for you to do so.
I am an employer, and I have counselled staff through time off for various reasons, depression included, and had I felt disgruntled or unsympathetic about it I would not have been allowed to show that or let you know that. To give an employee the notion that I did not approve of their recovery and not to actively encourage it would be professional misconduct on my part. Your employer has not only an obligation towards your welfare and recovery by facilitating that by whatever means reasonable, but can not pressure you about it in any way and must actively encourage it as a duty of care towards you and so as not to add to it further. It is wrong of the head to be obviously unhappy or unsympathetic about your condition. It is right for you, and indeed an obligation on your part, to let your relevent managers know if there is a problem and what steps can be taken to alleviate it.
You have some lovely blessings in your life. Your children and your partner, who love you very much. Try to concentrate on this and feel the strength of their love for you as a reflection on the person you are and will be again. You can give yourself the things you need to get better and enjoy your life again. It is very difficult but better times will come and recovery will come.
