There is another possibility - what you have described is the behaviour common to children suffering from extreme anxiety - specifically "selective mutism". And yes, her behaviour outside the home will appear "behaved" when, in fact, she just might be "stifled from fear". Then, when your daughter returns to a perceived "safe" environment, her stresses are released and "all hell can break loose". We lived this scenario for several years. The best site on the internet re this information is "selectivemutism.org" - I might suggest you peruse this site (especially the FAQ's) to see if these descriptions remind you of your daughter. If so, then the issue is more than just behavioural. Please let us know the results of your reading. I wish you the best .....
The striking difference in your daughter's behavior is an indication to you that the parent/child interaction should be the focus of intervention. You should refrain from yelling, and instead be calm and persistent. You are correct in pursuing the SOS strategy. It will be effective, but remember to implement it just as it is described.