Two problems:
1. Add series gate resistors. This controls the risetime at turnoff, which limits how much trouble you get into with inductances (increasing switching loss instead). At 100Hz, you probably don't need a proper gate driver at all; a level translator would suffice (e.g., just a few BJTs to switch 12V instead of 5 -- or use logic level FETs?). That is to say, by the time you're looking at 1kohm gate resistors, your peak gate current can only ever be 10mA or so, and a freaking several-ampere driver becomes absurd.

That TC4xxx thingy can drive gates in the tens of
nanoseconds. That's over
a million times faster than your waveform! It's a wonder you saw a spike at all on that scope shot -- the transients might be < 0.001 of a pixel wide, so it's very lucky to see them at all.
The random appearance or absence of spikes is a consequence of aliasing on the scope -- quite simply, most of the time, it doesn't happen to sample the input voltage at the exact moment the peak is its tallest. To correctly resolve them, you must zoom in on the rising edge, as tightly as possible, probably with a timebase well below 1us/div. Then you will see all the spikes and ringing in their full, horrendous glory.
2. You don't show the complete clamp circuit.
(2a. Good on you to put in a clamp circuit at all!)
With an even slightly inductive load, the instant the transistor(s) turn off, drain voltage rises, and keeps on rising (past whatever +V is on the far side of the load). The diode must be placed as close to the transistor as possible, so it can do its job as soon as possible. But a diode alone doesn't solve anything; +V needs to be stable, too. So you also need bypass caps, as close as possible to the diode and transistor. For something in the power switching range, you might be looking at an electrolytic >= 100uF.
And one possible gotcha:
3. TC4xxx are only rated to 18V, so any supply spikes are a hazard. I recommend a TVS (at least P6KE or SMAJ size, unidirectional, 12 or 15V nominal rating) and good filtering (you have 4.7uF among others, so that's not too bad; some electrolytic bulk might be handy, but may not be necessary).
Note that, when a transistor dies, it typically goes three-way-shorted, which means drain voltage getting to the gate. Which usually destroys the driver. If it's not dying, the overshoot and spikes, and ground bounce, and stuff, can cause problems, not just to the drivers but the rest of the circuit. Layout is a concern; ground loop; etc.
Tim