Who should do the rituals of antim sanskar of a married woman - her son or her husband? And who should give the mukhagni?
Antim sanskar is also referred to as Antyeṣṭi (अन्त्येष्टि) is a composite Sanskrit word of antya and iṣṭi, which respectively mean "last" and "sacrifice". Together, the word means the "last sacrifice". Similarly, the phrase Antima Sanskara literally means "last sacred ceremony, or last rite of passage".
Regarding your question who performs the last rites of a married woman, well it depends upon the fact who exists for instance if the son is alive then he will perform the act, if none then husband performs the last rites.
Just quoting from wiki:
The last rites are usually completed within a day of death. While practices vary among sects, generally, his or her body is washed, wrapped in white cloth, if the dead is a man or a widow, or red cloth, if it is a woman whose husband is still alive, the big toes are tied together with a string and a Tilak (red, yellow or white mark) is placed on the forehead. The dead adult's body is carried to the cremation ground near a river or water, by family and friends, and placed on a pyre with feet facing south.
The eldest son, or a male mourner, or a priest – called the lead cremator or lead mourner – then bathes himself before leading the cremation ceremony. He circumambulates the dry wood pyre with the body, says a eulogy or recites a hymn, places sesame seeds or rice in the dead person's mouth, sprinkles the body and the pyre with ghee (clarified butter), then draws three lines signifying Yama (deity of the dead), Kala (time, deity of cremation) and the dead. Prior to lighting the pyre, an earthen pot is filled with water, and the lead mourner circles the body with it, before lobbing the pot over his shoulder so it breaks near the head. Once the pyre is ablaze, the lead mourner and the closest relatives may circumambulate the burning pyre one or more times. The ceremony is concluded by the lead cremator, during the ritual, is kapala kriya, or the ritual of piercing the burning skull with a stave (bamboo fire poker) to make a hole or break it, in order to release the spirit.