Electronic – Trouble with DC/DC (switching) converter

First, a lot of that ringing probably isn't actually present. The very high frequency components are making the scope show common mode bounce as differential mode signal.

Second, all switching power supplies will have switching noise on their output. Some of this will contain high frequencies. Linear regulators may have impressive input rejection specs, but that is done with active electronics with a finite bandwidth. The new input rejection is only valid for low frequencies, like a few 10s of kHz. That is why it's standard practise to preceed a linear regulator with a ferrite bead (chip inductor) when the input voltage is coming from a switcher. The chip inductor and regulator input cap need to be physically close, the loop kept small, and the loop currents carefully considered in layout. You don't want those high frequency loop currents running accross the main ground plane.

Added:

I didn't notice that the second supply was a switcher too, but that doesn't really change anything. The high frequencies from the first switcher pulse edges are apparently making it thru the second supply whether linear or not. Try the chip inductor followed by cap straight to the ground of the second supply, not the general ground. This of course needs to be a ceramic cap, as big as reasonable for the voltage. A second smaller cap with better high frequency response might help a little too.

About common mode ground bounce. The ground is no longer a single lumped node at high frequencies, and not all at the same potential as a result. Sometimes whole sections of ground and power together can experience common mode bounce. However, what I was referring to was this common mode bounce in the scope. High frequency common mode signals can show up as differential mode signals. Dave, this was a lot of the problem in your similar question, and is likely part of the answer here too. Remember how things looked a lot better when you connected the scope probe directly to the output with a cap accross is and no place else. However in this case a downstream circuit is failing, so enough of the noise is real enough to be a problem.

I can't tell easily from the layouts what is actually routed where. One of the important things with switchers is to contain the large and high frequency loop currents. Make sure they don't run accross the main ground plane. Each switcher should have its own ground net, and that net should be tied to the main ground in only one place. That keeps the local currents local since only the net in or out current can flow thru the single connection point.

If you are 100% sure about the schematic you provide I would estimate the transformer to be a certain type of 1:4 or 1:5 job, depending on the smoothing capacitor and current drain.

If then, again you are 100% sure about the schematic not doing anything fiddly with the generated 40kHz on any other point (another winding? The incoming "+5V"?) this is an exceptional candidate for replacing with an isolated DC/DC module.

A very good reason to build this like they did is that in mass production the components may be cheap compared to a 1W5 avg / 3W peak DC/DC module.

Another very good reason is needing the resulting 40kHz wave at another point, or secretly tapping off another voltage somewhere. So you do need to make absolutely sure you don't interrupt anything but the 5V to 15V conversion.

The safest thing to do is leave the 15V regulator in place and replace the remaining circuit by a DC/DC unit that makes (one way or another) at least 18V, since we do not know the ripple requirements on the output. If it's just a gate voltage (and you can absolutely verify that it is) 100mVpp on 15V won't be much of an issue and you can go for 15V DC/DC blocks. In the latter case you may need to add an extra capacitance on the output (with or without Schottky and/or small resistor) to make the module's regulation less susceptible to the MOSFET's peak gate current.

If you have a floating bench top supply that does a nice 15V and/or 18V I strongly suggest you try it with that at a conservative current limit shortly to see if that works okay, since you can know and control the parameters with those and what happens upon a mistake with a DC/DC module is always a bit guess work.

Another thing to be very weary of is that the PIC might turn the auxiliary DC/DC off by stopping the signal and you may have to account for that in any of the possible fixes, since then it may assume its "off-ness" at other points in control loops. So certainly consider that in any further research.

As to the "laboured" square, that's possibly explained with the parallel capacitor, though I would say you'd still want some kind of a protection zener to prevent the MOSFET from getting into dangerous waters. If there is none of that at all, that is your first clue they might have not spent enough time on the DC/DC design, IMHO.