^
The attached is the current requirements of Phuket Immigration Office for an extension based on Marriage. Although, as we all know, differing IO's can have variations of what's required, Phuket has the reputation of being straight up.
Marriage (M) – Phuket Immigration Volunteers
So, applying for a 60 day non O whilst in the UK, on the basis of visiting family. Think you'll need to have copies of your marriage certificate and wife's ID card (your daughter's would also be useful, Thai passport if she doesn't have one yet).
The banked monies need to be in a your name only account (joint AC not accepted). I guess that the quarantine requirement will still be in force when you do eventually travel, plus the Covid specific insurance and less than 72 hour negative Covid test certificate.