1. DHCP: Use Static IP:MAC Address Mapping
If your Pi is not maintaining a persistent IP address, you can create a static IP:MAC address mapping on the DHCP Server (probably your router). Then, every time the router see's your Pi's MAC address, it will assign the same IP.
2. DHCP: Wrong IP Pool being used by DHCP Server
If your Pi is being assigned an IP from a completely different subnet, check that the appropriate DHCP pool is being served on the router's interface the PI is getting IP addresses from.
3. Colliding Subnets:
Ensure that Your PC & and the Pi are on different subnets on each end of the RDP connection. For example, if your PC is on 192.168.1.0/24 and the Pi on the other side is also addressed on 192.168.1.0/24, things are going to get mightily confused....
I've got a small switch I connect my Pi's to. This switch is uplinked to a MikroTik router that has a DHCP server listening on ether2 which the switch uplinks to. The router issues IPs for PI's connected to that switch:
[Pi]-------------[8-port switch]-------------[MikroTik Router]
This is what it would look like in the MikroTik's Webfig interface:
I go to the "LEASES" section of the DHCP Server and find my Pi:
After clicking the Pi's lease, I'm presented with the option to "Make Static":
Having made the "IP:MAC Address" mapping static, I can change the properties of the lease if I care to:
Now let's review the IP Pool being served by the DHCP Server listening on ether2 that the switch is connected to is serving 192.168 or 10.0 IPs:
Ensuring the Pi gets an IP from a correct range and the IP remains persistent are problems you can fix on the DHCP gears using the above as a template. Obviously your router's interface will be organized differently, but this should be enough to get you looking in the right places and knowing what you need to tweak. HTH- T