C.K.
As for your daughter, she may very well not need a nap at 3 years old, but may instead need to sleep 12-14 hours/night. I say why NOT put her to bed at 5:00 p.m. for a week or two, and see what happens?? What do you have to lose. She just might sleep until 6:00 a.m. or 7:00 a.m.--wouldn't that be nice??
A well-rested child sleeps better. She's now not sleeping at night because she's chronically overtired. Once she's had a few weeks of healthy sleep under her belt, then you can slowly push back her bedtime to a more agreeable time.
My son is also 1 year old, and he naps anywhere from not-at- all to 2 hours in the afternoon. So, I don't think your son only napping for 1 hour is really problematic. As my son's naps decreased, his sleeping at night increased. Why not put him to bed early, too, and see what happens? My son goes to bed at 7:00 p.m., but if he hasn't napped at all, I put him to bed at 6:00 p.m., and then he sleeps straight through until 7:00 a.m. (I hope the noise machine you've ordered helps, too.)
Lastly, I'd say take a good look at both their diets. Read the labels on what you feed them, if you can't pronounce an ingredient and have no idea what it is, DON'T feed it to them. Even foods marketed to toddlers and labeled as "healthy" can contain dyes and preservatives.