I don't know that it's a very good idea for your father to put you and your sister as joint account holders on his accounts and on the title of your house.
If anything happens to your sister or your finances, you won't be able to claim bankruptcy. They will take your father's money and his house. Even if you and your sister are financially responsible people, you never know what might happen (like a medical catastrophe) that could put you in a financial bind.
You should get power of attorney for his finances so that you can make financial decisions for him if he is unable to do that for himself.
The trust will make it much easier for you and your sister to inherit your father's assets once he passes away. You will pay much less in taxes and probate, so it will be worth the attorney fees to have this set up. Plus, it makes it easier for your sister and you to divide the assets in the event that there are unequal sums of money in the would-be joint bank accounts when your father passes away.
It's good that you are thinking about this now while your father is still healthy. My father didn't do anything other than draw up a will. He suffered a stroke and was in a persistent vegetative state for about a year and a half until he died. My siblings and I had to go through hell and high water to liquidate his assets so that he could get the care that he needed.
I am so sorry for the loss of your mother. I lost my mother when I was a child, and the loss is still so heartbreaking.