Praise be to Allaah.
We ask Allah, may He be exalted, to reward you immensely and
to bestow His blessings, both apparent and hidden, abundantly upon you and
to grant you beneficial knowledge and righteous deeds. We congratulate you
for the blessing of Islam that Allah has bestowed upon you and for your love
for Islam and for following its teachings in the manner prescribed by
Allah.
So long as you are afraid of severe consequences for showing
your Islam openly, you are not obliged to show it openly in front of your
parents. Allah will accept a person’s Islam even if he does not show it
openly when he is not able to do so. So long as a person has entered Islam
by uttering the twin declaration of faith (Shahaadatayn), he has to
adhere to its teachings as much as he is able to after that, without causing
any trouble for himself that may prevent him from continuing to follow this
religion. Allah tells us that the believer from the family of Pharaoh
concealed his faith from Pharaoh and his people, as Allah, may He be
exalted, says (interpretation of the meaning): “And a believing man of
Fira‘un’s (Pharaoh’s) family, who hid his faith said…” [Ghaafir 40:28].
Some of the Sahaabah (Prophet’s Companions) became Muslim in the early days,
when the Muslims were in a weak position in Makkah, and the Prophet
(blessings and peace of Allah be upon him) encouraged them to conceal their
Islam for fear of trouble. One of these people was the great Sahaabi Abu
Dharr al-Ghifaari (may Allah be pleased with him). The Prophet (blessings
and peace of Allah be upon him) said: “O Abu Dharr, conceal this matter and
go back to your own land, then when you hear that we have begun to prevail,
come (and join us).”
Narrated by al-Bukhaari, 3328
As you broke the fast on that day because of your parents’
presence, as you mention, and your fear of dire consequences if you did not
break the fast, then you are excused for breaking the fast. But you have to
make up that day whenever you are able to do so and are confident that no
harm will befall you as a result. And you do not have to offer expiation for
that day.
We ask Allah to enable you to do that which pleases Him.
For more information please see the answer to question no.
165426
And Allah knows best.