Have you checked to see if the services issues occur only in your house or does it occur outside?  A new SIM card might help, but it will only help so much if the building's construction is reducing the signal to unusable levels.  There can be number of factors that will reduce the signal.  The terrain (trees, hlls), nearby buidlings, your own building construction and wiring can degrade the signal and block the line of sight between you and the nearest cell tower.  You can also look on www.antennasearch.com to see where the nearest towers are in relation to your location.  One option you can consider purchasing a Network Extender from VZW if the signal issue occurs only in your home.  Verizon Wireless doesn't give them away for free like other carriers.  Why I don't know.  You do need a decent landline internet service and a postpaid account with Verizon Wireless for the Network Extender to work properly.  Also if your phones support it, you can look into the Wifi calling option.

If that is not a solution for you, you can always speak with your wallet and switch to a carrier that does provide the strong cell signal in your house and the other areas you usually frequent.