Hi,
DNS updates on multi-domain with single DHCP is tricky. It will work but with certain limitations.
When updating the host record, DHCP server searches for a DNS server which is authoritative for the zone matching the domain name of DHCP client.
So if DHCP client is a member of new domain, DHCP server will look for a DNS server which is authoritative for the zone .
Read the section: DHCP in a Multi-Domain AD Forest from this link for detailed tested approach
https://social.technet.microsoft.com/wiki/contents/articles/51810.windows-server-integration-between-dns-and-dhcp.aspx
I would recommend separating the subnets and dhcp server per domain to avoid any potentials issues.