Answer
Wa `alaykum as-Salamu wa Rahmatullahi 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 sister, first of all we admire your feelings and commend your concern to bring up your children in accordance with the Islamic Shari`ah.
As for your question, you should clearly know and believe that hijab is considered mandatory in Islam.
Hence, you have to bear the courage to apply what Allah Almighty, your Creator, has imposed on you. Fearing people will not benefit you much, especially in the Hereafter.
Also, clothing styles fall under the religious and personal freedom which is guaranteed by all laws and constitutions of the world.
So, seek help from Allah Almighty and be brave in facing and shouldering the consequences of your right decision and be sure that He will definitely help you.
In his response to your question, Sheikh Ahmad Kutty, a senior lecturer and an Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states:
A Muslim woman has to wear hijab as soon as she reaches puberty, as indicated in the Qur’an, the Sunnah of the Prophet (peace and blessings be upon him) and the consensus of Muslim scholars from early ages of Islam up till now.
Allah Almighty says:
“O Prophet! Tell your wives and your daughters and the women of the believers to draw their cloaks close round them (when they go abroad). That will be better, so that they may be recognized and not annoyed. Allah is ever Forgiving, Merciful.” (Al-Ahzab 33:59)
In another verse, we read:
“And tell the believing women to lower their gaze and be modest, and to display of their adornment only that which is apparent, and to draw their veils over their bosoms.” (An-Nur 24:31)
The Prophet (peace and blessings be upon him) said to Asma’, daughter of Abu Bakr (may Allah be pleased with them): “O Asma’! Once a girl reaches puberty, nothing of her body may be seen (by non-mahrams) except this and these, (he pointed to his face and hands while saying so).” (Narrated as weak ‘da`if’ by Abu Dawud)
With regard to your specific case, if you fear harm from those around you, then you may simply wear modest attire. If, however, you don’t fear any physical harm, you should summon the courage to stand for what you believe to be right. Islamic rules of modest attire in Islam include covering the entire body except the face and hands.
You should convince yourself of the importance of observing the rules of your religion and then ask Allah Almighty to help you overcome the inhibitions and remove your anxieties.
Allah Almighty knows best.