So you would make a button column in the INTAKE row and the formula would be something like this:
AddRow([Evaluations],
Evaluation.Owner,
AddRow([Owners], Owners.Name, thisrow.OwnerName, Owners.PhoneNumber, thisrow.OwnerPhoneNumber... etc etc),
Evaluation.Dog,
AddRow([Dogs], Dogs.Name, thisrow.DogName, Dogs.Breed, thisrow.DogBreed... etc etc),
Evaluation.Issue, thisRow.issue... etc etc)
Then you would set up an automation to push that button whenever a new row is added to Intake.
Does that make sense?