Airport Express can't handle multiple devices
This is normal, especially with older routers like the AirPort.  TCP is a “greedy” protocol, it will take all that it can when it can, so if you have a node (computer on the network) consuming lots of bandwidth other nodes experienced high latency and low throughput.
You may or may not remember, but places with free WiFi would often have horrible connectivity when the “business” crowd showed up with their VPN clients.  Basically, they would hog the bandwidth whether they were transferring lots of data or not.  Many places blocked VPN traffic because if this.
You need a new, modern router
The way you fixed this was you configured QoS (quality of service) for individual clients and protocols.  More advanced routers would  allow “packet shaping” where the router would limit the amount of bandwidth per node and/or protocol.
Modern routers take care of a lot of this for you automatically. Many can allow you to prioritize  traffic.  For instance! http/https takes highest priority, but email takes lowest. More advanced routers (I use pfSense) allow much more granular control to limit bandwidth by node and by protocol/application.  A regular retail, consumer grade router should be enough for your needs.