Keeping you data under control is very important Ilickstamps. As a parent myself, I know the concern. When connected to WiFi your mobile data should not be used. However, if WiFi connections is lost your mobile data will kick in. Is the data turned off on the Iphone 5c when connected to the WiFi? Settings>Cellular>Cellular data. You can verify what is using your data here: http://vz.to/1z1kvRW .
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there can be Wifi dead zones and interference from other wifi or even microwave ovens to have wifi drop. If that happens, the phone will switch to cellular data seamlessly. You can set many apps to only use wifi. For example, on an iPhone you go to settings, and scroll down to the youtube app. On the selection is "use cellular data" turn that off. I believe android has the same setting, but others will need to chime in. You can also turn off cellular data when at home.