Hi,
The term "had a home in the UK" includes your parent's home, as it is a place to live.
RDRM11330 - Residence: The SRT: Second automatic UK test
The guidance above advises "This test will be met if there is at least 1 period of 91 consecutive days (of which at least 30 must fall in the relevant tax year), when: the individual has a home in the UK and spends a sufficient amount of time in that home, and in addition, the individual has no overseas home, or has an overseas home or homes in each of which they are present, (for no matter how short a period), on fewer than 30 days in the tax year, (the permitted amount of time)."
Thank you.