I don't doubt that these mothers are going through a unique trauma, but it seems like a few of the case studies are making the issue completely about themselves.
It's sad when a child is rejected by their parents because they aren't living up to what is expected of them.
If this is a phase, I think the most important step is to make sure the child feels loved and accepted. Follow the APA's recommendation and support your child's wishes. That has been shown to cause suicide rates to drop drastically in the teenage years. Making it about losing your daughter, raises the chance of losing the child completely, if not by estrangement, it could be permanent like suicide. Only the most disturbed of individuals would prefer a dead child to that of a child who happens to be transgender.
This isn't about the parents anymore.