Is it permissible for a pregnant woman to bring her mother to live with her to help care for her baby and with childbirth, especially since she lives in Italy?

If the intention is for the mother to travel without a mahram, then it is not permissible due to the prohibition of the Prophet (peace be upon him). The prohibition becomes even stronger if the travel is to lands of disbelief, which the Sharia has forbidden residing in. For travel to such lands to be permissible, it is stipulated that there be safety from temptation and the ability to perform the rituals of the religion.