This is a tough question since it's not really a treatment question like the ones people usually post here.
I used to work in critical care research and I saw many families who were unwilling to let go of family members who were in dire straits. While I am not drawing a parallel between those situations and your Dad's cancer, the one thing I will say to you is this:
Be sure you completely understand why he feels the way he feels and why you feel the way you feel before you decide to encourage him to go back on chemo. I he is not sure then explore the options, including side effects and quality of life issues with he and his doctors in great detail. If he is still unsure then you could express your wish that he have the chemo. But, and this is going to sound harsh,if he has made a fuly informed decision and he is at peace with that decdion then you need to make sure that you are not being selfish in encouraging hm to undergo the rigors of chem again so that you can have him in your life a little while longer. That is askig him to suffer for you and your feelings because you don't want him to be gone.
Please don't misunderstand this next part but your Dad is 76 and he probably knows what he wants. If he chooses to have a better quality of life for a shorter period of time and he makes that decision with a sound mind I would recommend that you honor it and spend as much time with him as you can. Record his life stories, in his own voice, so you have them to share with your children and grandchildren and honor your Dad with your love and support of his decision no matter what it is.
I hope you understand that this message was sent with love and concern. I have just seen so much suffering I felt that I had to respond.
God Bless...
Juliet