I had 6 inch roots(!) from the last semi permanent dye I had put on my head in the hair dressers.
I've got a sachet of Wella Shaders & Toners here which is a wash in, wash out hair dye that's supposed to last up to 3 washes (Lasts 1 wash for me, Weeks for my DM who has really porous hair). Here's the ingredients list for the plum shade:
Aqua (Water)
Sodium Laurareth Sulfate (Found in shampoo, soap, etc)
PEG-3 Distearate (Low concerns re: Organ System Toxicity)
Sodium Chloride (Salt)
Cocamidopropyl Betaine (Associated with Irritation & Allergic Contact Dermatitis)
Alcohol Denat (Moderate Concerns re: Organ System Toxicity)
PEG-200 Hydrogenated Glyceryl Palmate (Low concerns re: Organ System Toxicity)
PEG-7 Glyceryl Cocoate (Low concerns re: Organ System Toxicity)
HC Red No. 3
Parfum
HC Blue No. 2
Polyquaternium-10 (Low concerns re: Ecotoxicity)
Methylparaben (High concerns re: Endocrine (reproductive system) disruption, Moderate concerns re: Biochemical or cellular level changes)
Sodium Hydroxide (Moderate concerns re: Organ System Toxicity, Low concerns re: Irritation of Skin, Eyes or Lungs)
HC Red No. 10
Sodium Benzoate (Low concerns re: Organ System Toxicity)
Propylparaben (High concerns re: Endocrine disruption, Low concerns re: Ecotoxicity)
Potassium Phosphate (Salt)
Benzoic Acid (Low concerns re: Organ System Toxicity)
HC Red No. 11
Butulphenyl Methylpropional (High Concerns re: Persistence and bioaccumulation, Moderate Concerns re: Organ System Toxicity, Low Concerns re: Endocrine disruption)
Tocopherol (Natually occuring chemical compound related to Vitamin E)
I don't think I would be happy putting this stuff on my child's hair unless it was their decision and they were capable of going into a shop to buy it themselves. Christ, I've now got second thoughts about using it on myself!!!
OP, YABU. You are right that your son and your future daughter are your responsibility, but that means you should act responsibily towards them. You say that it was only on the tips, but the dye could easily have come into contact with his skin even if you'd used a cap (which I doubt a 3yo would stay still for long enough). You were also BU for swearing at the lady at the creche (staff or fellow parent?) as she may have just wanted to let you know that it's not advised to colour young children's hair.