Plumbing Follow-Up
The toilets are toiling again and the washer has been replaced and installed properly this time.
The drain on the washing machine was definitely not installed by my Dad. One of the joints involved silicone caulk, covered in electrical tape, and topped with duct tape. After I cleared that away, a drain auger revealed that someone had dropped a screwdriver down the drain which significantly reduced the efficacy of the system. The air admittance valve was not installed properly and it caused a minor leak rather than admitting air to prevent siphoning. The handle of what had been a screwdriver that was retrieved from the drain was a cheap department store tool. My Dad would never have considered using such a tool, much less owning it. My Dad only bought Craftsman or Xcelite screwdrivers.