I think derailer systems are easier to work on than IGH, which is a good thing b/c they generally need more maintenance. IGH hubs need some lube, but a basic 3 speed is easily adjusted and will hold adjustment for a very long time, so if you keep the chain clean/dry, you can run it for a very long time with very little maintenance. Sprockets as well as chains last a lot longer on SS and IGH set-ups, b/c it's hard on parts to shift a chain across a cassette or multiple front sprockets. Chainline stays optimal for the UGH as well, if set up properly. By their very nature, derailer systems will have the chain oriented diagonally which contributes to wear.


But, yeah, if my derailer system acts up mid-ride, I can typically fix it/tune it on the side of the road or trail in short order, and keep rolling. OTOH, if an IGH blows up, i'll likely need to get it home to take a crack at it.... and, if it's one of the less user-friendly ones, i'll either need to take it to the shop, or just lace a replacement hub into the wheel. (Sturmey-Archer no longer makes the most reliable IGH, but they are tops for availability of spare parts, ease of rebuilding, and transparency from the manufacturer on how to lube them properly.)

FWIW, if your wife is going for a vintage/cruiser/Dutch-bike aesthetic, the derailer system won't look the part as much as an IGH will. I truly believe that your best bet will be to find a larger-sized step-thru Raleigh Sports (or similar Sturmey-Archer AW-equipped 3 speed) for about $100, then pay a competent bike shop to overhaul it. Spend the other $200 on some accessories, a new saddle, and dinner out--- so long as y'all ride to the restaurant.