That's the biggest, best performer in her budget. She can sacrifice the dedicated card, and go intergrated, but that'll make gameplay even worse. I'm not sure how demanding the Sims 3 is, so she may be able to.
This is not a small laptop by any means, and not sure exactly how "portable" it is, but it's one of the biggest screens. This is meant as a desktop replacement. It has pretty good integrated, one of the best I believe. If she wouldn't mind refurbished, she could get it for less than her budget. It's $700 new.
Amazon.com: Toshiba Satellite P505D-S8000 TruBrite 18.4-Inch Laptop (Black/Silver): Computer & Accessories