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If Microsoft SQL Browser is using broadcast, then you cannot split them in to different VLAN since broadcast cannot across subnets.
Here is a similar thread discussed before, you could have a look:
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However, based on my research, it seems that some third-party routers can relay broadcast between 2 subnets.
Since typical router behavior, by default, does not allow broadcast forwarding, a client's UDP broadcast requests cannot reach a target server on a different subnet unless the router is configured to forward client UDP broadcasts to that server.
For your reference:
Please Note: Since the web site is not hosted by Microsoft, the link may change without notice. Microsoft does not guarantee the accuracy of this information.
Best Regards,
Candy