I have three thoughts on the matter. Maybe four...maybe 5. Some, or all, maybe don't apply to your situation.
1. The first photo has the chain sucked all the way around to the top of the cranks, and my brain goes to "why did they keep pedaling that long?". It's like when you are driving on a mountain road, overshoot the corner and are now in the gravel, and you keep your foot on the accelerator for one second...two seconds, and keep driving off the cliff. Try to hear and feel it happening and stop. Don't drive through the gravel and off the cliff
2. Chain suck is always much worse when you shift the front under load at low RPMs. When I taught new riders how to shift the front, I told them the front shift should be dictated by the terrain, and should therefore be obvious and easy to see and easy to anticipate. The rear is for "feel". On a 24/38 in front, the 24 is for pedaling up steep inclines. The 38 is for everything else. The classic mistake that inexperienced riders make is they are cruising along at a good clip, get into a really high gear because they are cruising along fast, then they stop at a red light. Then the light turns green and they are grunting with all their weight on the pedals going "darn, this gear is way too high!" and slam the front shifter while still pedaling with all their might. The solution to that is shift to a good start-up gear before you come to a stop so there is no shifting under load. The axiomatic truth of front shifting is that the lighter your pedaling force the better the front-shift will be.
3. What happens during chain-suck is that the chain moves over from the OLD ring to the NEW ring. For a fraction of a second the chain is engaged with both. Pedaling force kind of rams the chain into position on the NEW ring. If the teeth are lined up just right that can make a pulling force on the part of the chain that is still on the OLD ring. That can make the chain "stick" to the teeth of the OLD ring, and so instead of rolling off the ring, it stays stuck to the old ring and gets pulled up. Hooked or otherwise damaged teeth can make a ring "stickier". A chain that's a hair too narrow can make a chain more likely to stick to the ring and get pulled up. The way the two rings are clocked to each other can influence the way the teeth line up. I'd recommend you make a black mark on the 24, and on the crank arm. Then remove the 25 and clock it by 1/5th a turn. Many 24T rings have an arrow on them and that arrow is intended to line up with a similar feature on the 38. Look for those features, see if they are lined up, and experiment with different orientations.
4. Big picture, it seems that a good mechanic who you trust should look at the bike, and a good rider who you trust should review front shifting techniques with your wife. One way to think about it is that you should always shift the front before you need to. The rear is for shifting right now because you are in the wrong gear right now.
5. These issues are one contributor to why so many bikes today are 1x. Rear shifting and front shifting are entirely different actions, and rear shifting is close to fool proof. The only truly fool proof front shifting is no shifting.
Finally, never cross chain small-small, EVER, even as an intermediate step to get to another gear. Small-small is hot lava. Stay away from the hot lava. Only use the 24 when using the bigger half of the cassette.
Best of luck getting it sorted.
Bill Lindsay
El Cerrito, CA