OK, firstly welcome to the forum, you've posted in the wrong section
You start the post by saying everything used to work until you replace the router, a router that is not supplied by VM .. so to me that suggests the new router is the problem.. VM will not support you as they did not supply the router and sending out a new modem is just a waste of everyone time.
As for sending someone out to sort it, the techs are only trained and allowed to deal with VM equipment and that doesn't even cover VM's routers, so that's probably just been a way for someone to get you off the phone.
You're saying the wireless keeps dropping in and out ? the modem has nothing to do with the wireless, so the issue is 100% Belkins.