Answer
I have great sympathy for your wife and how she feels, as I too often wish that I could just die so that I can escape the horrors that are so much part of our lives today.  I also know that the kind of illness she is suffering is painful and saps the strength, so that one is very tempted to just give up.  But I am convinced that she is wrong and you are right.  If we look at her reason, it is actually a very selfish reason.  In this she is considering only her own position and not the position of four children growing up without a mother, and a lone father trying to be both mother and father to them.  Let’s look at the passage in the Bible that talks about love, and see how love is defined.
 
1 Corinthians 13      4 Love suffers long and is kind; love does not envy; love does not parade itself, is not puffed up; 5 does not behave rudely, does not seek its own, is not provoked, thinks no evil; 6 does not rejoice in iniquity, but rejoices in the truth; 7 bears all things, believes all things, hopes all things, endures all things.
 
It says that love does not seek its own, which means that love is always focused on others, not on our own desires.  It also says that love bears all things and endures all things, which means that we should be willing to put up with any pain and suffering, if it will help others.  In your wife’s case that love should be focused on what is best in the situation for the children, and that is to do anything to prolong her life in order to give the children the best possible start in life.  Let’s now look at the first few verses of the same chapter:
 
1 Corinthians 13       1 Though I speak with the tongues of men and of angels, but have not love, I have become sounding brass or a clanging cymbal. 2 And though I have the gift of prophecy, and understand all mysteries and all knowledge, and though I have all faith, so that I could remove mountains, but have not love, I am nothing. 3 And though I bestow all my goods to feed the poor, and though I give my body to be burned, but have not love, it profits me nothing.

It is our love towards God and others that defines us as Christians. If we do not have this love, as it says above, “it profits me nothing”.   True love would want the best for a family, even if it means a transplant operation and more pain, but also a probable healing and extension of life. So, in spite of my sympathy for your wife, I have to agree that God would want her to fight for life, in order to help her children have the best life possible.
 
Matthew 22     37 Jesus said to him, “ ‘You shall love the LORD your God with all your heart, with all your soul, and with all your mind.’ 38 This is the first and great commandment.39 And the second is like it: ‘You shall love your neighbour as yourself.’ 40 On these two commandments hang all the Law and the Prophets.
 
1 John 2:6   He who says he abides in Him ought himself also to walk just as He walked.
John 13     34 A new commandment I give to you, that you love one another; as I have loved you, that you also love one another. 35 By this all will know that you are My disciples, if you have love for one another.”
 
Now of course you have the job of convincing your wife in a spirit of love, not rubbing her nose in it, but lovingly explaining what the Bible has to say, and what God’s expectation is of us as Christians.  I’ll be praying for you and your wife, and hope that the end result will be a wonderful life for your whole family.

We trust this Bible based answer brings you comfort and peace.

Jesus loves you very much.

Blessings, love and prayers,

The New Zealand Christian Foundation Team