You certainly have a lot going on in the home. Can you diagram the home and where you will be using the internet/LAN from, what clients will be using the internet/LAN for each room diagrammed, as well as where the modem and router are at. Also, are there coaxial cable outlets in any/all of the rooms you will be using internet/LAN?
There are a variety of ways to accomplish your goal which may include adding Wireless Access Points including those called "entertainment bridges" for higher performance needs, Powerline plugs, MoCA plugs, or installing Cat5/Cat6 cable.
You may also consider a new router if you have clients on the LAN that have a NIC adapter card that can do up to 450 Mbps, but you may not see significant increases in throughput over your current 300 Mbps router except close to the router and typically only on the 5 GHz band (unless no one else in your area uses wireless 2.4 GHz).
You could experiment on where you place the router to see if that helps wireless performance.
You might want to connect all clients capable of connecting on the 5 GHz band by assigning them to the 5 GHz band (as long as performance remains appropriate). In this way, there will be fewer clients vying for bandwidth on the 2.4 GHz channel.
It could be a neighbor(s) are also using the same wireless 2.4 GHz channel and both of you using the same channel at the same time slows you (and them). Maybe trying a different channel (1, 6, 11) could improve LAN performance.
An electrical device (phones, radio-controlled devices, baby monitors, anything!) whose signal bleeds into the channel you are using on the 2.4 GHz band could be causing a slowdown. These can be difficult to figure out without special equipment, but you can try unplugging electrical devices till you find it/them.
You may also need more bandwidth from your ISP, either by upgrading your internet "speed" or by purchasing a secondary line.
You may need a combination of two or more of the above.
Like anything else, solutions abound if you have the money. Otherwise, tweak your equipment as best you can given your wallet and the limitations that your home presents to network nirvana.
Also for consideration - maybe the children can internet less, do homework and chores more, and let mom and dad have the bandwidth for WoW.