Your setup -as you described it- seems both incomplete and already quite complex, comprising several special use devices and running a dockered Pi-hole. That makes it difficult to understand where your problem lies. 
At the moment, it seems your problem is not specifically tied to Pi-hole, but rather to your network setup.
While this forum is good at solving Pi-hole problems, there are probably better places to get support on network configurations for specific devices like Synology routers or NAS systems and Unifi controllers.
So my advice will be limited to pointing out a few general issues where I think -based on what info you provided only- your understanding is lacking (if just by a tiny bit 
- apologies if you already knew the lot):
Make sure you have exactly one DHCP server on your local network
You neeed to identify and/or decide which machine (and software) is acting as DHCP server in your network. It seems you have at least three candidates in your network for this role:
Your RT2600ac router, your DS718+ NAS, and Pi-hole.
You did not specify whether your Unifi controller is just software or another piece of hardware, and you did not mention a modem (RT2600ac lacks DSL and broadband) - you should consider those also if you have them.
Only one of them should be your DHCP server - make sure DHCP is disabled on all other devices.
Understand the difference between upstream (or WAN) and local (or LAN) DNS servers
Your local DNS server will be used by your local network clients for host name resolution. Normally, it will be announced to a client by your DHCP server, but can be set manully on each client device. Only a local DNS server can know about the host names of devices in your local network.
Your upstream DNS server is a DNS server that is used by your local DNS server (e.g. a router or Pi-hole) for resolving public host names on the internet. Your ISP will routinely announce its own DNS servers to be used by your modem or router. Most devices will allow manual configuration of upstream DNS servers,
Understand the (non)-significance of defining multiple DNS servers
Most DNS configuration UIs will allow you to state several DNS server addresses, usually a primary and one or more alternative ones.
It's important to note that employment of a certain DNS server for any given DNS query is totally at the device's discretion.
If you want to enforce the use of a specific DNS server (like Pi-hole), it must be the only DNS server on the list.
Don't change the ports Pi-hole uses
Clients within your network will use the standard DNS port (53) to contact a DNS server by default.
If you do change ports, be sure you know why you are doing this, and how to ensure that your network configuration will actually re-route DNS queries to the correct port.
Understand how Docker isolates networks
Make yourself familiar with Docker's networking options. Depending on how you configure Docker, you might push Pi-hole into a network that is not readily accessible by your local clients. This is especially true if you decide to make Pi-hole your DHCP server. In that case, be sure to read Docker DHCP and Network Modes
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(Dont' forget to click for details above)
I am not familar with neither your hardware nor the software it runs, so you have to resort to more knowledgable sources on how to convert my hints into actions specific for your devices. Probably try Synology's forums or manuals for a start.
Once you've sorted out your network setup, you are very welcome to return here, should you encounter problems getting Pi-hole up and running 