Getting to an older version of a backup

Something happened to my iPhone backup. Basically, using it prevents my old phone (iPhone 7) and then a new phone (iPhone SE) connect to the Internet. Everything is fine with a Restore until it starts to load in the back-up. Then I lose my internet connection (even though it shows me connected to a router). Placing my SIM card in a Droid phone, allows it to connect to the Internet. This happens both at home and at a T-Mobile store. I would REALLY like to get to an earlier version of the back-up so I can get to some my old apps and data. Any suggestions??

Thanks!