Help with email to SW

[Earthsomg]

Hi, am desperately looking for advice.
At a recent meeting, a social worker asked me to confirm whether my child's father and a joint tenant were the same person. I wasn't able to answer clearly at the time as my child was in the room and I didn't want that conversation happening in front of him.
I've since written a follow-up letter clarifying things: the father and I co-parent and share a tenancy, but aren't in a relationship. His everyday name differs from his legal name for unrelated reasons, and I've offered for the social worker to verify his identity directly with him.
A few questions:
•Is it reasonable to suggest meeting somewhere neutral, like a park, so my child isn't present for that conversation but the social worker still gets to see us both?
•Am I required to disclose unrelated family matters (e.g. an inheritance dispute with siblings) if they're not about my child?
•Any risk in clarifying something in writing after not answering clearly the first time, even though it was to protect my child from an adult conversation?
I haven't reached a solicitor yet and would appreciate any guidance before I send anything. Thank you.