Will it run sims 4

maryreed17​  The game shouldn't crash on either computer if you use too much cc, provided that cc isn't itself broken in some way.  It actually shouldn't crash at all, again aside from broken third-party content, on any computer that meets the requirements and where the graphics settings aren't turned up too high, and where there isn't some underlying system issue.

The gaming vs. non-gaming laptop designation has its uses, but the important details can get lost.  The two things that really matter are the hardware and the cooling.  You can have gaming-level hardware in a non-gaming laptop, it's not all that uncommon, and then the only important question is whether the laptop can properly cool that hardware.  It doesn't matter what category the laptop falls into beyond that.  People who say some game will crash on a "non-gaming laptop" without going any further are taking a shortcut that can lead to misrepresenting the situation.

The Acer Aspire you linked has the lowest-level gaming graphics card currently available, but again one that is capable of handling Sims 4 on high-ultra to ultra settings.  The laptop is also presumably not defective and is built to be able to cool its components, so although I wouldn't let it sit on a blanket while playing, I would also not expect overheating to be a major issue.

Having said all that, the Asus is more powerful, even if by a relatively small margin.

This really is your call, and I guess your mother's.  Neither choice is bad, and if the extra money is a major factor, you can choose the cheaper option without worrying you'll lose too much performance because of it, let alone not be able to play.