Should I include stepchild on my citizenship application?

I am marriage-based green card holder and will be applying for citizenship very soon (married Dec 2011, conditions-based green card April 2012, removed conditions March 2016) Under the CHILDREN section, I am confused. My husband is a naturalized citizen and has a 10 yr old child from a previous relationship (was not married - the child is a US born citizen). He does have a financial arrangement with his ex, sees his child regularly and they live about 20 mins away (child sleeps over every weekend). However they do not have any court/ child support DOCUMENTATION as they have agreed to arrangements they made together on their own . My husband does not claim the child on his tax return (which we file jointly every year) and only the child's mother claims the child on her taxes as a dependent. I have two questions - should I list the stepchild on my application? And if so, what documentation should I provide since my husband can only provide is his own bank statements to show he transfers the mother money monthly to their joint account which they set up together years ago? (and is this enough proof?)