My dear sister surely you and your Mother have suffered a lot and I pray that Allah recompenses both of you abundantly for all the suffering and oppression you have both been through. There are great rewards available for those who remain patient through trials and hardships long as long as we do not blame or ask Allah "why"? for we must accept his decree as surely he knows best as to the tests each of us goes through in life. He recompenses greatly to those who are patient for his pleasure. My dear sister we will surely be tested through our families particularly our parents. Through them there is huge rewards for treating them with kindness regardless of how they treat us. It is no doubt an extremely tough test but know that Allah does not burden a soul more than they can handle.
So regardless of how our parents treat us then we must always maintain the utmost respect and honour for them in return as is decreed by Allah:
And your Lord has decreed that you worship none but Him. And that you be dutiful to your parents. If one of them or both of them attain old age in your life, say not to them a word of disrespect, nor shout at them but address them in terms of honour. (Qur'an; 17:23)
Remember that by us giving our parents goodness in return for however they treat us then we are only doing so for the pleasure of Allah. However it is not permissible to sever relations with one's parents. Even Mushrik (Those who associate partners with Allah) parents are deserving of respect then what of Muslim parents?
Have you ever tried to speak with him whilst he is in a calm and good mood about your true feelings? It maybe worth trying to get him to open up about his own feelings in a loving and gentle manner so as to appeal to his emotions and explain to him the impact his abuse is having on you and your Mother. Try and get him to open up about why he behaves in such a manner and what the both of you can do to help him feel better about himself and the situation he finds himself in.
You must also try and focus on the good aspects of your Father. Although there is absolutely no justification for his actions but maybe he also went through a very difficult and abusive childhood which has had a detrimental effect on his own psychological development growing up. It maybe that he is also going through manic depression and does not know how to handle it and so takes it out on you and your Mother. What is certain is that he must certainly feel trapped and alone in the predicament that he is in. Even though he puts up a touch and angry front then surely deep down he is also going through much pain inside.
Try and keep out of his way when you are aware that he is in a bad mood and do not answer back to him lest his anger gets worse. Show him love in return for his anger and his heart will eventually soften. When we react badly towards anger then it only fuels fire further. Also my sister know that when a person is angry they do not know what they are saying. Although he makes abhorrent remarks about your looks but it is only because he is angry and so he does not know what he is saying. No Mother or Father would truly ever really mean to say such remarks. When people are angry then they just want to hurt the other person with hurtful remarks but deep down they do not mean it. Afterwards when he has calmed down I am sure he regrets it. So just ignore whatever comes out of his mouth in anger and walk away. Do not take such words to heart as he does not really mean it. Feel sympathy for him as deep down he is very unhappy and his heart is not at peace. Surely we should fear the divine punishment for ourselves, parents and families in this world and/or the next.
I would also recommend that you play Surah Baqarah in the house often. Do many prayers in the house to ward off shaythan's presence and fill the home with the remembrance glorification of Allah. Recite the Qur'an in the house and knowledge books and lectures. Remind your Father in a gentle manner with wisdom and tact of our inevitable death and of the day of Judgement. Try and watch good Islamic lectures around him of someone that he listens to.
Do you have any elders within your family or relatives that you can ask to speak with him? Someone who he will respect and whose advice he is more likely to accept? If not then approach a good reliable local scholar to discuss these matters as maybe he can speak with your Father.
Make much Dua for him and your Mother especially during these blessed days and nights. Ask of Allah to put love and mercy into his heart and to guide him. Ask of Allah to save him from the punishment of this world and the next. Beg of Allah for his assistance and to give the you both patience inshaAllah.
Finally always have in your mind that the Reward of going through difficult trials and hardships immense:
Narrated Jabir ibn Abdullah (Ra) Allah's Messenger (Sallallahu Alaihi Wasallam) said,
"On the Day of Resurrection, when people who have suffered affliction are given their reward, those who are healthy will wish their skins had been cut to pieces with scissors when they were in the world." (Al-Tirmidhi #1570)
So remember: Victory, relief and ease comes with patience through distress and hardship
The Prophet (Sallallahu ALaihi Wasallam) said,
"Know that victory comes with patience, relief with distress and ease with hardship.” (Ahmad)
Please go through the following thread for many resources of patience through trials and hardships:
How To Get Through Hardships & Trials in life!