hi Will, thx for the update ...
so it sounds like indeed there _are_ some incompatibilities between the lighning-to-ethernet adapter and the usb-to-ethernet adapter. but the MacBook as well as the Dell should also have a "regular" (gigabit?) ethernet port, don't they?
have you already tried to connect both using these ports (just for testing)?
if you send us the details to i'm sure we can get a much clearer picture of your issue (how do you connect to the internet, used IPs on all ethernet ports, ect.).
also please make sure you actually are using 2 separate network ranges for internet and the direct connection, both are using different class C network (network mask 255.255.255.0) and the direct connection is using a private network range (e.g. 192.168.100.x where x is between 1 and 254 and different for each device).
hth, cm