Wa alaykum assalam wa rahmatullah wa barakatuh

 

In the Name of Allah, the All-Merciful, the Mercy-Giving

 

All praise is due to Allah. Peace and blessings be upon His Messenger Muhammad.

 

As long as this appointment is necessary, you have to be in the company of your mother and sister. Friday Prayer is not obligatory on travelers. So, if you cannot pray Jumuah, you have to pray Zhuhr instead; and there is nothing wrong in this case.

 

As for your cat, you have either to provide necessary food for it during this period or to let it go and look for food.  The Messenger of Allah (peace and blessings be upon him) said, “A woman entered the Hellfire because of a cat which she had tied up, neither giving it food nor setting it free to eat from the vermin of the earth.” (Al-Bukhari and Muslim)

 

Almighty Allah knows best.