Certainly there is a solution to blocking adult content and other objectionable parts of the internet on my children's phones ***that can be implemented from within Verizon's network*** i.e. through Family Base? I have seen responses from your support team suggesting we take their phones, remove all browsers and add a new special browser, but that is a band-aid, not a solution. Parents want to block the inappropriate traffic at the network level. (If you do not have a solution, I suggest you contact the people at OpenDNS and work together to make this a reality.)
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I mentioned OpenDNS because Verizon Family Base does not appear to have a solution for blocking Internet sites based on content. On my home network, I can set the router to use OpenDNS's DNS servers and the devices logging into the network will not be able to visit sites that have been tagged as falling into the off-limits categories I have selected.
You mention making that line a child line... what does that do? I have designated it as a child line in Family Base; is this different?