Supiii,
Day I sounds good. We are happy with Vedettes de Pont Neuf for the Seine cruise. About one hour, narrated (live, not a recording), inexpensive, can reserve a time online. Sit up top for best viewing. Get in line a bit early to snag a top deck seat. Bring something for warmth unless it is hot. You can check when sunset is that day and reserve a cruise for then to see the Eiffel Tower get lit up. We have used Vedettes several times and feel it is the best for this type of cruise.
Day 2 Yes to Notre Dame (even earlier time if you can). I don't recommend walking (gradual uphill) the Champs Elysees...too many chain stores and chain restaurants. It is best looking down from the Arc de Triomphe toward the Place de la Concord with the Tuileries beyond. And after the Louvre and the Tuileries, you may want to put your feet up for a while. I am guessing your 3:00 Louvre tour won't end before 5 at the latest. Then a minimum half hour through the Tuileries (at a good clip), and you won't feel like walking the whole length of the Champs Elysees. You might want to rethink this afternoon. (Could you get an earlier tour at the Louvre, say 1:00?) Since you aren't m useum people, I would pick one of the many smaller museums instead of the Louvre. Do you have any particular reason for choosing it? Maybe the Orsay instead?
Day 3 Versailles is truly an all day thing. I like it a lot, but with 4 days I would choose a less demanding side trip. Chartres is lovely and has a magnificent cathedral. Also, Vaux-le-Vicomte or Fontaunebleau are good day trips. You could get back in time for your Montmnartre tour if you left Paris by 8:00 or 9:00 and left these places by 3:00. Each of the three takes about an hour by train, plus or minus 15-20 minutes. (P.S., Go inside the Sacre Coeur cathedral to see the mosaics while you are in Montmartre.)
Day 4 I don't know the Lafayette shopping mall, but I love the beauty of Galeries Lafayette Hausmann, near the Opera Garnier. The Opera building is magnificent, with a wonderful Marc Chagall ceiling. Tours are on offer sometimes. It is a short walk to Galeries Lafayette from there, and Printemps is nearby too. Of course the truly high-end shopping street, IMO is the Rue Du Faubourg-Saint-Honore. I would definitely combine the Opera house visit with a visit to Galeries Lafayette. Look up while in the store and admire the ceiling. Go to its rooftop for a nice view of Paris, including Sacre-Coeur on Montmartre and the Eiffel Tower (in the distance).
Other possibilities which I might consider (leaving out museums, sadly) would be strolling along the left bank across from Notre Dame and checking out the bouquinistes for inexpensive mementoes, going to Ste. Chappelle (wonderful!), resting at a cafe with a coffee or aperitif and watching Paris walk by, sitting on the Champs de Mars and just staring at the Eiffel Tower, going to the Rodin Museum just to relish the sculptures in the gardens (I have been 7 or 8 times now and never tire of it). If a museum were to call to you, I would choose the Cluny or the Orsay. And Paris has many concerts at churches, etc., and Ste Chapelle also.
Hope you and your mother have a great time. Amusez-vous bien!