Wa `alaykum As-Salamu waRahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
Dear questioner, we would like to thank you for the great confidence you place in us, and we implore Allah Almighty to help us serve His cause and render our work for His Sake.
Answering your question, Dr. Muhammad Salama, PhD, Islamic Studies in English, Associate Professor at the Faculty of Islamic Sciences al-Madinah International University (Mediu), states:
May Allah grant you patience for your loss and help you in raising your kinds.
It is a great responsibility to educate and raise this number of kids. Those who advise you to remarry keep in mind your needs as a man for a wife and your needs as a father for someone to share this responsibility with you.
This, of course, because they suppose that you will find an understanding and helpful wife; but you might fear of not finding the right woman and thus bring more trouble to yourself and your children.
Marriage in Islam is not obligatory unless you find it difficult to control your sexual desire and commit related sins as a result. Still the Prophet of Allah (peace and blessings be upon him) said, “He who can afford to marry should marry, because it will help him refrain from looking at other women, and save his private parts from committing illegal sexual relation; and he who cannot afford to marry is advised to fast, as fasting will diminish his sexual power.” (Muslim)
I would advise you to keep the door open for the possibility of remarrying. Perhaps one day you find a good woman who takes care of you and your children. Meanwhile, take care of your children and seek the help of Allah and pray istikharah before making any decision.
Allah Almighty knows best.