Baking – How long should I let the bread dough rise the second time

Damn, that looks good. I've never made this particular type of bread before, but here are some things that I do know which might help:

Butter is (roughly) 10% water and 90% fat, while lard is 100% fat. So if you substitute one for the other, you should adjust the amount of water in the recipe accordingly. The flavor will be a little different, but I bet either one would work.

I would not assume AP flour. In fact, I'd assume high-gluten bread flour. The gluten is what creates those fibers. It's the fat that keeps it tender.

This looks very similar to a brioche, so you might want to look at brioche recipes to learn some of the principles. One thing that most of them will tell you is to to knead the dough to develop the gluten fibers, and then add the butter. This I think is the key. I know that fat can keep gluten molecules from sticking together into strands, so if you add the fat later, you should wind up with strands of gluten surrounded by fat.

There are some previous questions with good answers like this one, or this that go into much more detail than I'm about to.

You said your bread didn't rise with the first rise, if you don't have a first rise you can't go onto the next step. If your yeast was old, or the temperature was cold in your kitchen or you used cold water in the dough, or the yeast came in contact with salt then its action could have been slowed down drastically and it would take much longer to get a rise. I've had a first rise take up to 4 hours in the past because of these factors. The times given in recipes are just guidelines, you have to be result-driven. Active dry yeast also takes longer than quick yeast to activate. When using active dry instead of quick yeast you would get better results by mixing it with the water before mixing in. I'd recommend using quick yeast as it's milled into smaller grains and you can mix it directly into the flour.

Of course your yeast may have simply been dead, or killed by salt or heat. Get some good fresh yeast and store it in the fridge to keep it fresh long-term.

Also, using all whole wheat flour isn't going to produce anything like a baguette. Whole wheat flour is very heavy compared to white flour and will take longer to rise. A half and half mix would work better. I'd recommend sticking to the recipe first, then gradually modifying it over time until you get your desired result.