There is no physical proof that Lindsay Clancy, rather than Patrick Clancy, committed the act of killing the children.
There are no fingerprints on the bands or the knife that identify her. The DNA on the bands is mixed family DNA and does not isolate her.
There is no independent proof the children were alive when he left the house for his 37 minutes of errands.
The case against her for the act itself was built on Patrick’s account of that night, not on forensic evidence that pointed more to her than to him.