Firstly, a tip of the hat to you sir for taking the time to give your kid an experience like this. Kudos to the bonding & resilience your instilling in them.
Here's a couple considerations:
1. Boiling is the most effective to kill any/all pathogens. A "rolling boil" for at least a minute should do it (a couple minutes even better). However, as someone noted above, boiling doesn't remove heavy metal / environmental toxins. You'll need a filter for that.
2. Chlorine tabs, liquid Chlorine bleach, or Iodine tabs. These are convenient, but only kill off bacteria & viruses (& maybe some protozoas like giardia). But, none of these are effective against protozoas like Cryptosporidium. And not effective against heavy metals / toxins. For these, follow the instructions on the bottle, or for liquid bleach use this website as a guide for ratios based on % chlorine in the bleach. ((And make sure its just plain 'ol bleach; nothing scented, 'color safe', etc)).
https://www.epa.gov/ground-water-and-drinking-water/emergency-disinfection-drinking-water
For Iodine & chlorine, you'll need to let it sit for at least 30 minutes before drinking, so if crossing a stream fill up your empty canteens & use appropriate doses so it's doing its thing while continuing your trek.
3. Cloudy water will take more time & resources to purify, so filtering it thru a thin cloth with charcoal can help remove some of the cloudiness & improve tase.
4. If you're going to be stationary for a day or two, the solar still will be a cool experiment to try. It doesn't produce a ton of water, so you may want to dig a couple of them. Some plants will make the water taste funny, so after producing the clean water may want to run it through a charcoal filter as well.
4. UV pen lights kill pretty much everything, but nothing for heavy metals / toxins. If the water is cloudy, or you don't stir it up enough, you may not kill all the bad stuff, so either filter first, or wand it longer. ((Also get from a reputable place; REI may be more expensive, but more peace of mind than Amazon...)
5. Filter systems. Look for something in the .01 micron range so it gets all the nasties, plus most of the heavy metals. And carry extra filters. Cloudy water will reduce life span, so clarify first if possible.
6. Med Intel. Look at what's upstream / uphill of your water source, & take that into account for what you'll need to filter out. If your water source is downstream of a pig farm, chicken farm, hay fields, solar farm, industrial sites, etc, your method of purification will need to account for what may be in the water. ((Also take into account other environmental factors, like if you're staying at a primitive campsite where people have been deficating on the ground / cat holes / slit trenches, there may be other hygiene issues such as pinworms in the soil))