Having had a chat with Buba1947 in WPF room, I've concluded that she's actually got a 1-1 relation split table in database that she's actually trying to show as such in the split data grids.
First, I recomend to use the INotifyPropertyChanged interface in the base class. Maybe you use it and forget write it in the sample code. For make this with MVVM patter, you need to implement a ViewModel for both data grids.
Let's call it in our example BothGridViewModel, you may call it as you want. Then in this view model you need the collection of all person, let's call it AllPerson, then you need to have a property of Person type, when you will have the selected person in the grid, let's call it SelectedPerson. It will be something like this.
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