As has been mentioned in the comments, you are free to supplicate to Allah for your needs. However, a relevant Qur'anic supplication with regards to your family's success in the hereafter is found Surah al-Furqaan, verse 74:
رَبَّنَا هَبْ لَنَا مِنْ أَزْوَاجِنَا وَذُرِّيَّاتِنَا قُرَّةَ أَعْيُنٍ وَاجْعَلْنَا لِلْمُتَّقِينَ إِمَامًا
"Our Lord! Bestow on us from our wives and our offspring who will be the comfort of our eyes, and make us leaders for the Muttaqun"
In his Tafseer, Ibn Katheer explains the expression "the comfort of [one's] eyes" citing several sources:
يعني: الذين يسألون الله أن يخرج من أصلابهم من ذرياتهم من يطيعه ويعبده وحده لا شريك له
It means: that they ask Allah to bring forth from themselves a progeny who would be obedient to Him and worship Him without associating anything as a partner with Him.
قال ابن عباس: يعنون: من يعمل بطاعة الله، فتقر به أعينهم في الدنيا والآخرة
Ibn 'Abbaas said: they mean [by their supplication] that [their wives and offspring] engage in acts of obedience to Allah, which would be a source of comfort for their eyes in this life and in the Hereafter.
قال عكرمة: لم يريدوا بذلك صباحة ولا جمالاً، ولكن أرادوا أن يكونوا مطيعين
'Ikrimah said: they do not seek companionship or beauty through this request, but rather that they should be from those who are obedient [to Allah].
As a side note
Every rak'ah (unit) of prayer requires a Muslim to make a supplication to Allah for guidance and steadfastness upon the Straight Path, in the form of the last two verses of Surah al-Fatihah:
اهْدِنَا الصِّرَاطَ الْمُسْتَقِيمَ صِرَاطَ الَّذِينَ أَنْعَمْتَ عَلَيْهِمْ غَيْرِ الْمَغْضُوبِ عَلَيْهِمْ وَلَا الضَّالِّينَ
Guide us to the Straight Way - the Way of those on whom You have bestowed Your Grace, not (the way) of those who earned Your Anger, nor of those who went astray.
It is perhaps due to the Muslim's severe need for guidance that this supplication is built into every unit of prayer that they offer.