Sorry you're having to face such a terrible predicament. Can you get several high quality HEPA air filters and place them in the main rooms where your toddler goes? What about confining the cats to one part of the house (maybe with access to an outdoor enclosure so they spend less time inside)?
"To close your eyes will not ease another's pain." ~ Chinese Proverb
“We must not refuse to see with our eyes what they must endure with their bodies.” ~ Gretchen Wyler