There are a number of places in the Bible where reference is made to families and the relationship they have with God.

Unfortunately, in some cases, Scriptures have been hijacked for the purpose of strengthening a particular religious group at the expense of the family. This practice dates back to the religious leaders of Jesus' day when elderly parents were deprived their due support because their children claimed that everything was devoted to God. (Mark 7:11)

Cult leaders in modern times have misused Scriptures by pointing to statements of Jesus such as Luke 14:26: "If any man come to me, and hate not his father, and mother, and wife, and children, and brethren, and sisters, yea, and his own life also, he cannot be my disciple."
There's also a statement which sounds like Jesus actually promotes and rewards the break-up of families: "And everyone who has left houses or brothers or sisters or father or mother or children or fields for my sake will receive a hundred times as much and will inherit eternal life." (Matthew 19:29)

Once, when Jesus was teaching the people, His own family members, mother and brothers, came to see Him. Listening to how Jesus responded, some people get the idea that He couldn't care less about them; He seems to redefine the family as now being made up of His disciples, along with anyone who "does the will of my Father in heaven." (Matthew 12:46-50)

On another occasion, while looking into the future, Jesus proclaimed, "Do you think I came to bring peace on earth? No, I tell you, but division. From now on there will be five in one family divided against each other, three against two and two against three. They will be divided, father against son and son against father, mother against daughter and daughter against mother, mother-in-law against daughter-in-law and daughter-in-law against mother-in-law." (Luke 12:51-53)

Drawing from these verses, many religious leaders have instructed their followers to separate themselves from their "ungodly" family members and join together with their new-found spiritual family. In so doing, they nullify the Messianic promise given in the last verse of the Old Testament, "He will turn the hearts of the fathers to their children, and the hearts of the children to their fathers." (Malachi 4:6) Just the opposite of this transpires - children are separated from their parents and vice a versa for the sake of furthering the goals of the religious organization.

On the other side of the coin, there is the command, "Honor your mother and your father," a commandment which was included in the commandments given to Moses. This was on the first stone tablet that has primarily to do with our relationship with God, placing the relationship with parents on a high level of importance. This injunction was reiterated by Paul, "'Honor your father and mother' - which is the first commandment with a promise." (Ephesians 6:2)

In the Gospels, after Jesus delivered the man possessed by a "legion" of demons, He sent him back home to give the good news to his family: "'Go home to your family and tell them how much the Lord has done for you, and how he has had mercy on you.' So the man went away and began to tell in the Decapolis how much Jesus had done for him. And all the people were amazed." (Mark 5:18-20)

Also in the Gospels, there are several examples of parents bringing their needy children to Jesus. There was Jairus, whose daughter was terminally ill, a woman from Syria who came begging Jesus to heal her daughter, a father whose son was demonized; and we have the group of parents who brought their little children to be blessed by Jesus. All of these are examples of believers caring for their family members by bringing them to Jesus of by praying for Him to intervene.
Later in the New Testament is the wonderful promise given to the correctional officer in charge of Paul and Silas - "Believe in the Lord Jesus, and you will be saved - you and your household." (Acts 16:31)

In the household instructions, the "haustafel," the Lord is very much involved both with children obeying their parents as well as the way parents treat their children. (Acts 6:1-9) And Paul gives a firm word in the Pastor's manual, "If anyone does not provide for his relatives, and especially for his immediate family, he has denied the faith and is worse than an unbeliever." (I Timothy 5:8) Perhaps this instruction is related to financial provision, but if Scripture urges faithfulness in regard to the material things, how much more the spiritual.