I know this is a difficult and serious decision, and you are wise to look at it carefully and prayerfully. But if you know this would have been your mother's wish, and if your family agrees, then I believe it would not be wrong for you to instruct them to avoid extreme measures.
Medical science has given us many good gifts today, including the ability to prolong life in the face of disease and old age. The Bible reminds us that "Every good and perfect gift is from above, coming down from the Father" (James 1:17). But sometimes modern medical technology doesn't prolong life; it only delays death. When that is the case, we may actually be trying to do something God has not willed.
Let me be clear: Life is sacred, and only God has authority over life and death. I strongly oppose euthanasia (so-called "mercy killing"), and I believe we must do everything we can do to prolong life and bring healing. Thank God for the good care I trust your mother is receiving but most of all, for the hope we have of heaven because of Christ's death and resurrection for us.
As a footnote, you should, of course, read carefully anything you are asked to sign, to be sure you understand it and agree with it. However, most documents of this type have been carefully drafted, with many safeguards to be sure they aren't abused.