How to connect a rectifier circuit (mains driven) with switching regulator MC34063?
First, your rectifier circuit is wrong because you're grounding D4 at both ends. You only need to ground one side, the other would be "floating". Since there is no such thing in SPICE in general (every node must have a connection to ground), add a 1g resistor across the ground and "floating" ground.

Second, your second circuit already has a DC source which supplies it constantly, from the beginning. The rectifier would be outputting a rectified sine, therefore the voltage at its output needs time to build up. You could try to cheat by making the input source a cosine and imposing initial voltages on the capacitors. Don't forget about the input transformer, though...

And third, your joined schematic uses the wrong rectifier circuit where D4 is still shorted.

No comments in rest, but if you correct these you should be able to simulate it. One note, though: if you open up some of the jigs in LTspice, you'll see that, for example, instead of using a full 50Hz, or 60Hz input source, Mike uses a 500Hz or 600Hz, and reduces the feedback and accompanying circuitry, accordingly, in order to not wat for a full 16.67ms or 20ms cycle.