Welcome to carp.com.
Firstly what you are doing is working, so don't complicate things, just stick with it. You are catching good fish up to a good size.
What you may find is that venues with bigger fish are not compatible with days only, so with family you might have to stick with what you have. However, if the club has lakes with bigger fish take your working methods over there and try them.
In terms of fishing tackle you could be spending silly money on gear you don't need, buzzers, new rods, new reels.
What you do need is decent sized landing net, unhooking mat etc.
You will get so many answers on what is decent gear, Shimano, Daiwa, Wychwood, Sonik, Nash, Fox, Delkim, the list is endless.
The best bet is to go into a tackle shop near you, preferably one who knows your venues, and see what he recommends.