Is it permissible for me to make a will that I be buried with my deceased father, knowing that there will be non-mahram men in the burial chamber?

Burial in underground chambers (fasaqi/saqaya) is a matter of scholarly disagreement:

- Those who prohibit it: They believe the default is for each person to be buried in a separate grave, and they forbid the mixing of men and women, as well as burying one deceased person on top of another before the first has decomposed. - Those who permit it: They allow it out of necessity, such as limited space, citing the Prophet, peace and blessings be upon him, who gathered two or three people in one grave at Uhud.

If it is possible for the questioner to be buried in a separate grave, then it is not permissible for her to stipulate in her will to be buried in those chambers. If it is only possible to be buried in them, then it is better for her to refrain from making such a stipulation, as the responsibility for burial falls upon the living.