You need to compensate yourself not only for your addition time but the fact that you will likely be feeding her dinner with your family which incurs an additional expense as well ... small piece of boneless chicken these days costs $2 at least not to mention whatever additions you add to it for dinner

I also charge $5/half hour for overtime over my 9 hour program day because they are no longer 'sharing my services' with other families to get that cheaper 'group daycare rate' during my business day, plus they are asking me to work 'overtime' which any other industry is paid premium wage to work and well I am not even charging 'minimum wage' so that is fair IMO AND most importantly they are cutting into my family time so it needs to be worth it to them too for me to consider doing it.

Personally I would not keep a daycare child over 'dinner' as that is our family time to connect about our day and discuss personal things about said day or to debate about issues in our community and so forth and I do not want family to feel they have to be 'cautious' about that time in case a child repeats something at home that is taken out of context or what not