What can I do for thirteen hours transit at Guangzhou with my three kids?

Steven, no, you don’t need it. You are able to use the 24 hour direct transit in Guangzhou. You may be required to apply for a temporary stay permit which is free of charge and then you can go to the city for a visit.
As far as I know, Yuexiu Park and Guangzhou Museum are free of charge.
You are advised to go to these restaurants: Guangzhou Jiujia (Guangzhou Restaurant), Taotao Ju Jiujia (Taotao Ju Restaurant), or Bing Sheng. You can taste the Cantonese cuisine there.