I think that the product you were thinking about was called Black Knight. I know that that was taken off the market just recently, although i am not sure why.
I have had great sucess with proventamite. I would not however, spray it directly on the animals. Especially baby snakes. If you spray it on the substrate and the enclosure it should do the trick.
Did the vet say why you shoudlnt use the oil treatment? Olive oil works great for suffocating the mites. As does soapy water baths. What i did with my BTS was: when i realised that he had mites, i immedieatly soaked him in a soapy water bath. (make sure that the amimal you are soaking is properly hydrated BEFORE you do this, so they dont drink the water)) Using a soapy water bath will make it so the mites arent 'water tight'. Alot of times, mites will survive normal soaks because they form air bubbles around them. Dish soap will prevent this.
Next, what i did was take him from the bath, dry him, and rub snake oil on him. Snake oil consists of all natural oils such as sunflower and tea tree oil. It serves to soothe the skin, as well as suffocate the remaining mites. Olive oil will serve this purpose just fine if snaike oil is not readily available.
Then, i would take my freshly oiled albeit angry skink and place him in a hospital tank. this tank was a 10g with a uth, proper lighting, and paper towel as a substrate and disposibal hides and water dish. This tank was rotated daily for one week. The rotation consisted of bleaching out with 10:1 water to bleach solution, a THOROUGH rinsing, replacing the towels and placing the towels and furniature into a plastic bag which was then sprayed with provent a mite and then tied and thrown away. This was done daily.
This was a rather extreme and agressive mite treatment, but with having all the animals that i do, i believe it was needed. When i put griff back in his home tank, i had changed out all of his bedidng and thrown out his wooden fixtures. I then (before placing the skink back into his tank) sprayed the entire enclosure (minus the water and food bowls, obviously) with provent a mite. I do that once a month now, just to be on the safe side.
The only problem i had was with the feeder insects. Proventamite is so strong that it will kill any feeder insects that are placed into the tank for a month. Griff ate a few of these, and then acted alittle weird, but he is ok.
i would try this. follow the directions on the can, and you should be fine....good luck to you and the babies

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1.0 ball python- Azazel
1.0 columbian boa- Brooklyn
1.0 red blood python-Hiss
1.0 peach phase thayeri-Sancho
0.1 creamsicle corn- Pandora
0.1 partial stripe ghost corn- Raven
1.0 Sunglow motley corn-Ernie
1.1 hognose- Pricilla and Odd
0.1 russian tortoise- Manja
0.2 leos- Boji and Kodama
0.1 beardie- Indie
1.0 BTS- Griffon
0.1 Iggy- Sunny
0.0.1 Red american toadlet
0.0.1 gray tree frog toadlet
4.3 bettas
0.1 pacific parrolet- Mishka
1.1 cats- Cairo and Oberon
2.4 ratties Rizzo, Bree, Blitzkreig, kaos, adelle, and shiloh