DHCP server on Windows Server or router/internet gateway?

Turning off the DHCP server on the Windows Server and using the DHCP server on your router/internet gateway is absolutely fine. It won't interfere with Windows clients binding to the domain hosted by the Server.
As long as your router/internet gateway is properly configured with the appropriate DHCP settings, your Windows clients will be able to obtain IP addresses and other network configuration information without any issues.
The only thing you need to ensure is that the DHCP scope on your router/internet gateway is properly configured to match the network settings of your LAN, including the subnet mask, default gateway, and DNS server addresses. Additionally, make sure that any reserved IP addresses or specific DHCP options that you had configured on the Windows Server DHCP are also set up on the new DHCP server.
Once the DHCP server is enabled on your router/internet gateway, you can go ahead and disable the DHCP server on the Windows Server. This can be done through the DHCP management console or by simply stopping the DHCP server service.
This change should have no impact on the domain binding or functionality of your Windows clients. They will continue to interact with the domain hosted by the Server as before.
Remember to update any devices that have statically assigned IP addresses to use the new DHCP server for addressing to ensure consistency across your network.