When using USB and external power, how should I isolate the grounds

I'm looking at and interpretting the schematics and here's my take.

1. If V_IN (external power minus a protection diode drop of probably about 0.7V) is above 6V, the USB power is cut-off from the 5V rail through a P-channel MOSFET.
2. If V_IN is below 6V then USB power will be connected to +5V through the MOSFET. V_IN will still energize the on-board 5V regulator, but since USB power and the regulator are at the same potential, they shouldn't fight each other , and you should be OK.
3. Looking at GND in the schematics, USB GND is tied to the 5V GND reference on the regulator, so again, you should be all set in terms of USB power not fighting your on-board regulated power.
4. In principle, having both USB and external power connected should allow you to source more draw a higher max current (the sum of the USB and your external power source).
5. Plugging in external power after USB power is already connected shouldn't do any damage, but you might get a transient dipping in +5V while the Op-Amps and MOSFETs settle, which might cause your Arduino to reset.

Anyway, my opinion is that it should be harmless. Not that I'm an "official source" :).

It sounds like your device needs more than the 100 mA it is guaranteed, but does not enumerated properly to request the extra current. You can get up to 500 mA from a USB port if you ask for it and the host grants it.

There is no guarantee that the host will grant the request, but desktop machines pretty much always do since they have plenty of power available. In fact, the desktop motherboard schematics I have seen show only a polyfuse between the 5V supply and each USB port. There is no active electronics limiting current. On those machines, you get the full 500 mA even if you don't ask for it.

Laptops however have limited power and therefore actively monitor and control USB power in most cases. Some machines may limit the sum of all USB devices to a certain current, or limit it more when running on battery only, or when the battery is low, etc. Note that USB powered hubs can't ever grant the full 500 mA since that is all they are getting themselves.

The reason your device won't enumerate anymore is because you broke the ground connection. All three lines D+, D-, and ground are required for communication. You can cut the power line if the device is self-powered. Self powered devices generally have no connection to the USB power line. That's perfectly OK, but they still have to connect via ground.