I went through similar in early October, found one on my pillow in the middle of the night, had them jumping on me when I was in the living room, nightmare. I'd been using Frontline on a subscription from PetsAtHome, the fleas are now immune to it. My first action was to get a prescription flea killer from the vet called Bravecto. I then flea bombed my house and vacuumed it. I last saw a flea (dying on my desk) in mid-November. You can do this.
First things first, when you say you re-treated Dcat with a stronger flea killer, you mean a prescription treatment from the vet, right? If not, get yourself and Dcat to the vet, stat.
If so, now that you've sprayed the house, just vacuum a couple of times per week and let Dcat go everywhere throughout the house for at least a few months. I'll explain why:
Fleas have a similar four-stage lifecycle to butterflies: egg, larva, pupa, adult. Vacuuming sucks up the eggs and larvae and spray kills the larvae. The pupae stick to the carpet and are impervious to the spray so they will survive to emerge as adults. The newly-hatched adults will hop into Dcat for a first meal that will also be their last, because the Bravecto in Dcat's blood will poison them. But Dcat has to go where the adults emerge from the pupae for the adults to be able to hop on.
A lot of people shut the cat out of rooms after a flea infestation, but that's counter-productive because the pupae will stay dormant for up to two years until an appropriate animal comes along, or else the adults will emerge and bite you or DC.