Hi,
In a domain environment, it may make environment more complicated and harder for troubleshooting.
And the load balancing for the AD services is supposed to be done by the client.
When we set DNS server for clients in domain, we can set 2 DNS servers or more for the clients in domain.
Preferred DNS server
Alternate DNS server
We may try to set part of the clients use the DC1 as preferred DNS server and DC2 as the alternate DNS server.
And the rest of the clients use the DC2 as the preferred DNS server and DC1 as the alternate DNS server.
In this situation, only when the preferred one is not available, the clients will turn to the alternate one.
Since all the DCs have the Integrated DNS ZONE, all the DCs have the same records for the clients.
Following link for your reference:
Load balancers and Active Directory
Best Regards,