Is it permissible for me to claim my inheritance from my deceased father and live in an apartment in his building without paying rent, just like the other heirs living there, especially since my husband is poor and his salary is insufficient for us?

The questioner has the right to claim her full share of her father's inheritance, whether she is poor or rich, and this is not considered an act of disobedience (to parents). The family must enable every heir to receive their lawful share. Also, whoever lives in an apartment belonging to the inheritance must pay rent to the rest of the heirs, and she has the right to claim her share of the housing rent for the past years, because the apartments are a right for all heirs, and they are partners in them according to their lawful share.