Can mold develop from having pets?

Mold grows from moisture so yes, pets can cause it. you kill it by getting rid of the moisture and cleaning with bleach.

Bleach will only kill mold on hard, non-porous surfaces.
It won’t work on a lot of common building materials like:
wood, drywall, insulation paper, ceiling tiles, etc.

If you rip up the carpet, pray for concrete instead of hardwood.

If you want pets without the mold, housebreak them.