Shock = chlorine
Stabilizer = cyanuric acid and this dissolves slowly
alkalinity up = baking soda (sodium bicarbonate)
The first and foremost important answer is what is your chlorine level. That will be the single biggest indicator when it is safe to swim.
The baking soda will have no immediate bearing and is safe, plus dissolves fast
The cyanuric acid (stabilizer) dissolves slowly - how did your husband put it in the water. Usually it is put in an old sock and left to dissolve (some hang in the pool, others in the skimmer basket - which is what I do). If there is white stuff all over the bottom of the pool, it is the cyanuric acid. I wouldn't let the kids swim with it on the bottom. I've been in a pool with stabilizer undissolved and I got very itchy. What I would do if I had mistakenly done this? I would vacuum up the powder into the filter (watch the pressures), and let it dissolve in the filter. There is a liquid form of stabilizer (still is cyanuric acid) and if you used that, I think you can just poor it in and go, but I never used the liquid stabilzer, so someone else may want to chime in on that.
Once the stabilizer is in a sock or in the filter dissolving slowly over a few days to a week, and you have your chlorine and pH at a safe level (you did read pool school?), your kids can go swimming.
However, before you do that, post your numbers, including at a minimum pH, Total and Free chlorine, Total alkalinity to get the final ok