First, let me say that I appreciate the love and care for your family.
However, you've spent way too long worrying about this, and way overthinking this.
You don't know that what you had on your scrotum was a wart, but let's assume for this post that it was. 90% of people will clear HPV from their bodies within 2 years. Since you've had no more symptoms, you can assume that yours has gone, and it was gone long ago.
Second, the strains of HPV that affect the genitals don't affect other parts of the body. There are hundreds of strains of HPV - plantar warts, for example, only affect the feet. The strains that affect the genitals don't affect the feet, legs, arms, hands, etc. What your kids have isn't because you may have had genital warts years ago. Those are totally different strains.
Even if you currently had active genital warts on your body, the warts your kids' have wouldn't have come from you. You wouldn't need a separate shower, or separate laundry, or special chemicals.
So take a moment and let it sink in - you don't have HPV any longer, if you ever did (and if you were diagnosed by a doctor, then you probably did, but you don't mention that). You weren't ever infectious to your kids, and depending on how long after you had the wart to when you met your wife, you may not have been infectious to her.
I think it's always a good idea to not share towels - people get fungal infections like yeast, jock itch, etc., and those can spread with sharing towels, but you don't need any special precautions for HPV. You don't have it any longer. Even if you did, you wouldn't be a walking biohazard. It's called a sexually transmitted disease because you need sexual contact to spread it.
I hope this helps.
"HPV infections usually clear up without any intervention within a few months after acquisition, and about 90% clear within 2 years."