The Acer Aspire V3 for $750 is not really a good option for playing games. The Intel HD 4000 was pretty decent at the time for an integrated graphics solution, however, it was considered a bit weak for games beyond low settings and low resolution.
The recommended HP laptop configured with the A10-5750m and the Radeon HD 8750m is pretty decent. AMD's APUs have less processing power compared to Intel CPUs, but their integrated graphics core is more powerful. The Radeon HD 8750m is a fairly decent mainstream GPU that should allow your daughter to play games at 1080p with a mix of low and medium graphics settings. Lowering the resolution will allow for decent performance with a mix of medium and high settings in many games that are not very graphically demand.
Laptops with both an AMD APU and AMD discrete graphics chip can operate in what's called "Dual Graphics Mode" where both the integrated GPU core (Radeon HD 8650g) and the discrete GPU (the Radeon HD 8750m in this case) can work together to provide better performance. That performance increases varies depending on the game and can range between a slight and decent performance boost. However, there is a caveat...
Dual Graphics Mode will only work with games that are DX10 or above. DX9 and below games will simply use the integrated Radeon HD 8650g and completely disregard the dedicated GPU (unless AMD has somehow changed this discrepancy). Skyrim is a DX9 so it can only be played with the Radeon HD 8650g, thus negating the benefits of having a dedicated GPU.
If you do not mind a refurbished or scratch & dent (cosmetic blemishes), then perhaps the Dell Latitude 3540 (business laptop) from Dell's outlet store is worth looking into. As of now there are 4 available for sale; 2 older models with the i5-4200u and 2 current models with the i5-4210u ranging between $669 - $719. The main difference is 100MHz between the two CPUs; so nearly the same performance. It comes with a 1920x1080 matte finish screen (not a glossy reflective screen). It has the "Radeon Venus Pro" which is more commonly known as the Radeon HD 8850m DDR5 (with maybe slightly slower clock speed). It also has a DVD drive.But it only has 4GB of RAM. I recommend buying a another 4GB stick and installing it yourself.
i5-4200u versions:
http://outlet.us.dell.com/ARBOnlineSales/Online/SecondaryInventorySearch.aspx?c=us&l=en&s=dfb&cs=28&puid=75f7be2c
i5-4210u versions:
http://outlet.us.dell.com/ARBOnlineSales/Online/SecondaryInventorySearch.aspx?c=us&l=en&s=dfb&cs=28&puid=1012be27
I bought a refurbished Dell Latitude 3540 from eBay back in January 2014 for about $500 and it works fine. Unlike most laptop nowadays which has a Windows 8 recovery partition on the hard drive, Dell provides you with the actual Windows 8 install DVD. The only thing I find lacking about the laptop is that the keyboard is not backlit. The laptop performs pretty well overall. While I have Skyrim I completed the game before I ever bought this laptop so I cannot say exactly how well it will run with the Radeon HD 8850m. Compared to nVidia GPUs it performs roughly equal to the GT 845m / GT 660m. That is what I would refer to as "high end mainstream" graphics performance. The only game I have actually played with the laptop though is Star Trek Online and it runs pretty smoothly.
Prior to actually purchasing the Dell Latitude 3540 I did some research and found out that some time between Black Friday and Christmas 2013 Dell was actually selling these laptops for $375. Therefore, whoever I bought the laptop from must have purchased it for that low price and made about $100 - $125 off of me. If I see the Latitude 3540 for $375 in Dell's outlet this year, then I will like pickup another one for myself.
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