I think it should be pronounced as いえ in this example. In my opinion, いえ emphasizes on the location or the house itself; while the うち is a concept of family or home. Also, うち can be used as "my" sometimes, like:.うちの会社、うちの家族.

We use both. 「うち」is for casual talking, like talking with friends.

I remember asking about it to my Japanese friend and she taught me that the words that resemble with うち in English is 'Home', as in one's OWN home. And いえ is just 'House'; it can be anyone's house. So, in your sentence too, I think うち will be the correct pronunciation. Hope that helps!