What are the qualifications for becoming an eternal family according to LDS teaching? I understand the LDS Church teaches the concept of an eternal family.  I guess the husband and wife have to have been sealed for eternity in a Temple marriage, and, therefore, have to hold Temple recommends.  I'm wondering if their earthly children also have to be Temple-worthy and if there are any other qualifications.

If one child is not Temple-worthy, then I'm wondering if that child is not a part of the eternal family in the afterlife, but perhaps would still have some relationship with his/her siblings and parents and possibly Temple-worthy children.

So, perhaps let us focus in on the specific qualifications for having an eternal family in heaven.
Becoming an eternal family requires living the gospel of Jesus Christ, which includes the following:


Developing faith in Jesus Christ.
Repenting.
Being baptized and receiving the Holy Ghost.
Enduring to the end.


"Enduring to the End" includes temple ordinances, such as the sealing (husband and wife or child to parents), and implies that one would be temple worthy. See the two quotes below, but essentially, the sealing  only remains effective when the parties involved are faithful to the teachings of Jesus Christ. You may find the temple-recommend interview questions helpful for a guide but, unfortunately, it's impossible to make a checklist of the complete teachings of Jesus Christ.

"Family members who accept the Atonement of Jesus Christ and follow His example can be together forever through sacred ordinances performed in God’s holy temples. Jesus gave to Peter the power to have things sealed on earth and sealed in heaven (Matthew 16:19). This same sealing power was restored to Joseph Smith. Mormon’s believe that they can be “sealed” or bound together through His power enabling them to live together in eternity." - http://mormon.org/faq/mormon-families

"In The Church of Jesus Christ of Latter-day Saints, the word sealing refers to the joining together of a man and a woman and their children for eternity. This sealing can be performed only in a temple by a man who has the priesthood, or the authority from God. According to Latter-day Saint belief, the sealing means these family relationships will endure after death if the individuals live according to the teachings of Jesus Christ."- http://www.mormonnewsroom.org/article/sealing