As far as I know, the proper sentence with "denna" is "Täcker denna försäkring hela familjen?". However, denna + definite form is used a lot in southern and western Sweden, so let's see what the moderators think about it :)!
"this" can translate either to denna or den här. But denna always takes the indefinite, and den här always takes the definite. So you can say denna försäkring or den här försäkringen, but not mix the two.