Let’s review the situation from your wife’s perspective. It is acceptable for her mother-in-law to sponsor her. You don’t need to prove a relationship between your wife and her.
Your wife may need to explain why just that university. We are assuming the key reasons, in addition to the ones you mentioned already, are you wanting to live together and cost savings. They are logical reasons. She needs to ensure she explains the reasons effectively during her interview if the topic comes up.
She doesn’t need to bring up Canadian Universities. It has no bearing on her US study plans; on the contrary, it may be a distraction.