This is a common misconception! (Unfortunately, too common)
Trusts do NOT avoid probate if the trust (revocable trust or living trust) was not funded properly before the death of the decedent.
For example, if mom created a Living Trust and all of her life insurance, bank accounts and other assets were paid out to the trust when she died (via a beneficiary designation), except for her house, the house would need to go through probate administration (albeit a relatively simple administration.)
Bottom line: Don’t assume that just because mom or dad had a trust, probate in Florida is completely avoided.