OP, if the sticking point is that neither of you know what to do with the window, I'm going to help out and give you suggestions that don't require replacing the window.
First, check the caulk around the window. If it's at all cracking, separating or getting brittle, strip it out and recaulk.
Second, apply new weather stripping around the window. Use the vinyl v-channel with adhesive backing (inexpensive and easy to apply), and follow a video like this to install it:
https://www.youtube.com/watch?v=sAPv9wdrNuo
Third, if you're still having drafts and temperature issue, replace the current window treatment with more insulating curtains or outside mount roman shades. It needs to cover at least few inches of the wall around the window when closed, and ideally you'd get something interlined for extra insulation (although this can get a little pricey).