Knowingly having to hurt a close person
Have you meditated on the reasons why you feel depressed being away from your hometown?

Is it friends and your social life in your hometown? Or is it some other reason?

If it is the friends and social life that's the problem, then you can try to make new friends. For e.g. why not join your local Buddhist community? For example, you can explore the Buddhistische Gesellschaft Hamburg e.V.. They seem to have a lot of interesting activities like group meditation, sutta studies and dhamma talks.

This way you can solve two problems in one go. It is not always the case that you have to choose either A or B. Sometimes, you can find a third way, C.

Drawing upon the example of the Buddha's life, he found that it did not work if he chose either over-indulgence or over-asceticism. Instead, he paved the middle way to enlightenment. The same theme can also be found in the Sona Sutta with the analogy of the strings of a lute playing music only when it's not too taut or too loose.

So, I suggest that you don't have to choose either your sanity or your mother's extraordinary dependence on you. Instead, you can pave the middle way, by solving multiple problems simultaneously.