I should be able to look into this later today. You can definitely do this with Axure.
You’ll want to add a column in your repeater for Order, putting a number for the original sort order. Then you can Update the repeater row(s) changing the number in the Order column and Sort the repeater by Order.
In the meantime, you can search this forum for “sort repeater” to see some examples and discussion about this.
Animating the movement of one row is trickier. You won’t be able to show movement of one row across other rows in a repeater, but you can fake it with a little bit of work.