Another advantage of the multiple router solution is you can have the kids attach to one and you&spouse attach to the other, with different rules (time/filtering etc) on each. Plus it gives you more WiFi bandwidth for you all to play with than just having one router/access point. (A wireless extender doesn't give any more absolute bandwidth, just a boosted signal which may help get the signal further).
We have the standard Sky (black) router on a high shelf under the stairs, linked to an EE one on the back bedroom window sill by Ethernet cable. The kids can only connect to the EE one, which has firewall rules that cut everything off 11pm - 6am. We can connect to both, so have 24/7 access in the house and day access in the garden. Both are 802.11n so plenty bandwidth for all. Works really well. Not hard to set up all details via Google.