Visa extensions in China

Theoretically speaking, your daughter and you are your wife’s family and you can apply for family Q1 type for your long-term stay in PRC.
But if the embassy says that you can only apply for an entry permit with multiple entries for a year and you get one with stay duration of 30 days for each entry, you need to apply for an extension 7 days earlier before it expires at the exit and entry administration of the local PSB.