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 Firaun's (Pharaoh's) family, who hid his faith saidâ¦ [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.
Reproduced from Islam QA