Is the prayer of one who performs tayammum due to an inability to perform ghusl more than twice a week accepted, given their living conditions prevent them from performing ghusl more often?

You are required to perform ghusl (ritual bath) from major impurity if you find water and are able to use it. If your aunt's husband does not permit its use, then you must seek water and search for it in nearby places, even if it means purchasing it at a reasonable price. You can also perform ghusl in mosques or university restrooms. If you do not find water, then tayammum (dry ablution) is your ruling.