Is it permissible for me to perform tayammum for prayer if I experience a wet dream before Fajr and my mother refuses to give me water for ghusl, and it is difficult for me to obtain water from neighbors and perform ghusl in their homes?

If you have reached the age of puberty (ihtilam), you have become accountable (mukallaf), and it is obligatory for you to perform ghusl (definition) (ritual bath) from janabah (definition) (state of ritual impurity) when its cause is present. Your mother's prevention does not absolve you from performing ghusl. You must perform ghusl with the water available in the house, and if there is none, then obtain it from outside, or perform ghusl in the mosque's bathroom if possible. Ghusl is not waived for you as long as you are able to obtain water. And it is obligatory for your mother to enable you to perform ghusl, otherwise, she would be sinful.