I don't think you can do it legally in the United States. Two of my kids were born while we were stationed in Bermuda, and have triple citizenship (US, Bermudian, and Great Britain). At the age of 18, if they opted to be Bermudian, they can keep all three. If they opt to be the Queen's subject, they can keep the Bermudian and give up the US. But if they opt to be a US citizen, they lose the other two.
Apparently there are a lot of other countries, I'm sure Canada is one, that allow dual citizenship, so she might be able to maintain US/Canadian dual citizenship as far as Canada is concerned, but coming the other way, she must renounce Canada as a part of the oath. And since she took the oath, renounced Canada, and now says in public that she didn't renounce Canada... it's time to take back that green card because she just broke some laws.