Your plan sounds pretty good to me, Brent. For what it's worth, I think that Citristrip offers a good blend of being relatively safe with reasonable working time. You do want to keep the toddler and pets out of the work area and have some ventilation while you are working with the stripper. You will want to wear gloves and eye protection then too. Mask the areas that you do not want to strip before you start. Citristrip will probably remove the adhesive residue and should work pretty quickly since there is not that much old finish on the treads.
I like oil based polyurethane on stairs since I think that it holds up better than water based. Do all 3 coats on every other tread and then come back and do the remainder. Dust will be your biggest enemy after the 3 year old so clean everything after you sand.