Soda and yeast both in pretzels

The existing answers already explain why yeast and baking powder won't work together. But even if they did, you wouldn't have a reason to use them.

You seem to think that fluffiness depends on the amount of gas produced by the leaveners. In fact, it depends on both the gas and the ability of the dough to trap that gas. If you produce too much gas (no matter whether through yeast or through baking powder), then the fluffiness will be less than when using the optimal amount of leavener. This happens because your dough cannot hold the gas and the bubbles break, resulting in the dough deflating like a punctured tire. So even if combining two leaveners would have resulted in more "blowing big" action (which it doesn't, see the other answers), you would not end up with a fluffier end product. If you want fluffy muffins, you have to use a recipe and a technique which is best capable of retaining the gas produced by the baking powder. The amount of gas production is not a bottleneck.

Unfortunately you're fighting bread-physics... Bread with a high crust:crumb ratio become stale faster than those with low crust:crumb ratios like large boules or miches. Their large surface area allows moisture to evaporate quickly and the starches dry up and harden. This is why thin breads like baguettes are traditionally "daily" breads, i.e. made/purchased to be consumed that day. Soft pretzels have an even higher crust:crumb ratio than baguettes.

Breads with extremely high crust:crumb ratios like hard pretzels, crackers, and hardtack are usually cooked to the point of being dry to prolong their storage capacity. These bread actually "stale" in the opposite direction by becoming more moist.

There are a couple of things you could try that might help a little. It might take a lot of experimenting to get something that helps, and you will likely still need to reheat the pretzels just prior to serving them to have the soft texture you're looking for. Without re-baking or light toasting there really isn't a way to bring back the original crust texture.

• Use pre-ferments to increase the concentration of a-amylase in your pretzels. Using a prolonged autolyse and/or sourdough starter can increase the amount of a-amylase in your bread which has been shown to slow staling.

• Incorporate conditioning ingredients like fat, sugar, malt, or honey into your dough. All of these slow staling.

• Try baking the pretzels at a lower temperature. The article linked above also mentioned that higher temperature baking leads to faster staling.

For storage, your best option is probably to allow them to cool completely (15-30 minutes) then place them in a sealed container at room temperature. Placing them in a sealed container before they are cool fills the container with humidity, which then coalesces and makes the crust soggy.