What happens if power sources are connected in violation of ideal circuit theory?
The first thing you have to realize is that "real" power sources are themselves not ideal. Voltage sources have non-zero internal resistances. Current sources can only produce a limited range of voltages (called compliance). So, for instance, connecting two voltage sources in parallel will look like 







simulate this circuit &ndash; Schematic created using CircuitLab

and in this case will produce a current which is equal to the voltage difference divided by the total internal resistance. Note that the circuit is now an "ideal" circuit.

There is no guaranteed way to tell how circuits will behave, unless you have a complete description of the components. Just as voltage sources have internal resistances, they will also have inductances, and in some cases will behave as if they have complex internal capacitances as well - batteries, for instance.

Plus, real power supplies will commonly only be able to source current, and are not at all good about sinking it, which requires the use (at least) of a diode when modelling the supply for real.

About the closest you'll get to your "non-ideal" connection is jumping a dead car battery. When connection is made, the strong battery will be called on to produce a lot of current, and in bad cases the current will damage the jumper cable. However, a discharged battery looks more or less like a resistor/capacitor combination, so after a while the current flow will drop to a much lower value.