Confirm the split
One name resolves with a public resolver and another does not. Testing both explicitly proves the problem is routing, not connectivity.
Resolve-DnsName -Name intranet.corp.example.com -Server 1.1.1.1 -ErrorAction SilentlyContinue
Resolve-DnsName -Name intranet.corp.example.com -Server 10.0.0.10 -ErrorAction SilentlyContinue
Get-DnsClientServerAddress -AddressFamily IPv4 | Select-Object InterfaceAlias,ServerAddresses