In summary, the joint custody of a child does not have a direct impact on the ownership or occupancy rules for either HDB flats or private properties in Singapore. The primary considerations remain the eligibility criteria set by HDB for public housing and the terms of ownership for private properties. You can find more detailed information on property ownership and occupancy rules on EdgeProp Singapore.
Thank you for your query with EdgeProp Buddy. As a reminder, I'm in Beta mode and it's always wise to seek counsel from a real estate professional for these types of matters.