Control of wired computer is outside the controls that Apple built into the Airport range.. and they stopped manufacture in April anyway.. so you will need to buy a new router at some stage. You can keep the airport as a wireless access point.
I have tested a number of routers with the demise of the Airport range.
Getting decent controls in a router is still not that common.
The best router firmware I have seen so far is the Gargoyle 3rd party... so you will need to apply this to a different brand of router.. eg Linksys WRT1200AC which are not expensive and have very reasonable specs. I have recently come back to this as my no1. recommend for what you are asking for. It does need that bit of a step to flash over the firmware which is a simple download and chose it as upgrade.
Asus high end router are very good with easy to setup controls and excellent wireless.. you need RT-AC88U or RT-AC86U or even better ones. I have hit an issue in a new setup so not every router works on every configuration. Be prepared to trial these things for a while and return them if they don't work.
I would recommend it as no.2
Synology are another one worth a look.. I am just not sure about its controls over wired computer.
Mesh systems are now also becoming popular but they have limited controls. Units like the Netgear Orbi can use ethernet backbone not just wireless. They are expensive for a whole set and perhaps limited cloud type setup.
A lot of people are moving away from the domestic type routers to more semi-pro .. particularly Ubiquiti. They have amazing controls and even the bottom end router models are very cheap. However they are just routers.. so you need to add a switch and wireless access points.. (WAP). An overall system.. router, switch and wireless AP will cost you a fair bit more than domestic all in one routers.. but easily outperform and outlast them. So the Ubiquiti system I bought was 20% more than Netgear top end Mesh system. Hugely superior controls though.
It is not as simple as domestic router though and I would only recommend it for someone who does enough networking to understand what they are looking at.. time and patience to learn the interface.. it is not hard but you have a steep learning curve going from simplistic apple routers to something like these.
You contract it out and get someone to build it for you as alternative.. rather then pretending to be a network engineer.
Depending on the speed of your internet there are also parental control devices.. if this is to help your kids. They can be worth looking into. They definitely slow down your internet but take control of kids devices very effectively. (Disney CIrcle products).