FX 6100 is a bulldozer CPU, 8350 is a Piledriver. Piledriver chips were a decent jump over bulldozer, most reviews at the time (2012) showing around 20% faster than the similar bulldozer part (8150 in this case). So you're getting two extra cores that will be a decent bit faster. It's still not a huge upgrade in terms of raw gaming performance, but it's there. Especially if you overclock the 83xx to 4.4-4.6Ghz
For what they are, the prices are still a bit much. I wouldn't spend over $100 on this upgrade. I would suggest a used 8320 or 8320E instead of the 8350 and save money. I bought my father an FX 8320 and overclocked it to 4GHz with no change in voltage (making it an 8350 right out of the box), and it's been rock solid stable for a few years now.
As for GPU, your mileage and answers will vary. I'm not going to suggest anything right now. This is a terrible time on the GPU market. I tend to avoid Nvidia products in budget machines. I personally grabbed a used Radeon HD7950 for $90 a couple years ago (last time bitcoin crashed and they flooded ebay) and it runs everything I care to play quite gloriously at 1080P to this day, though the power consumption is MUCH higher than a gtx 10xx card (check your PSU). You DO NOT have to spend big to get 1080P performance, though unfortunately right now GPU prices are ridiculous due to the "memory shortage" and bitcoin craze. Last year you could have had a Radeon 470 or 480 in some deals for 120-150 bucks and they are great for 1080P, but the prices now are absolute BS and I refuse to buy.
If you can afford it and just want a new card, I would grab the 1060. It'll max out any game I can think of at 1080P while consuming very little power. If you decide on a 1050, get the Ti, I don't understand why the 1050 only has 2GB vram, I have quite a few games that blow way past that at 1080P.
Get an SSD, everything you do on your PC will seem way "snappier". It's totally worth it, even if you just get a cheaper 128GB SSD for your operating system and software, games on your regular HDD. If her complaint with the computer is sluggish browsing or software, this will fix it.
Lastly you mention 8GB DDR3 but not speed. Is it running at 1333? 1666? I would take 8GB of 1866 over 16GB of 1333 any day. I don't see you getting much more performance out of the extra 8GB, but I haven't really been following modern games so take that with a grain of salt and go check benchmarks on the games she plays.
Sup. I like computers. Are you a computer?