Can someone help me to understand this issue with DNS updating slowly?

We have a very secure but antiquated system that’s used by everyone in the company. It requires a computer’s current IP to match existing DNS records in order for a user to login to it. That presents a problem when you have a laptop on Wi-Fi with an IP on one VLAN (10.x.1.x). Then the laptop plugs into a dock that has an Ethernet connection. Then the laptop gets switched to another VLAN (10.x.2.x). The DNS record still shows the 10.x.1.x IP. The user tries to login to this system. They’re denied access because they have the wrong IP. We get a help desk call saying they can’t login. Nslookup shows the 10.x.1.x IP. We have to remote to their computer, run “ipconfig /registerdns” and hope it works fast. Most of the time they can login immediately.

I’ve been told by the vets at my company and by the software vendor the only way around this is to give everyone a static IP. That’s gonna be a no from me, dawg. There’s one vet from another company that used the same system and gave everyone static IPs. I’ve learned to take what others say with a grain of salt because I’ve often found better methods to issues other people have given up on.

I’m new to getting this much into the weeds in networking and backend systems. Can someone explain why this might be happening and if there’s anything that can be done to speed up the DNS update process?