Octane Rating?

Just use 87 octane. If you have to buy 89 it just costs a few more pennies per gallon. 89 octane will not make the motor run better.

engines mix air and fuel, compress them and ignite them to produce power.
the more an engine compresses this mix, the more power it can extract from the fuel.
BUT, high temperatures and compression can make it so that the mix of fuel and air can detonate early and mess up the stability of the engine.
higher octane fuel is less prone to early ignition.
high performance engines are designed to use high compression to get the most power possible.
if an engine is designed to compress fuel and air to a point where running 87 octane fuel is fine, running 89 will not give you any benefits.
meanwhile, if an engine is designed to run with 91 octane and you use 87 then you have a problem as 87 will likely detonate before its supposed to thanks to the higher compression.

unless your mother is an engineer with direct experience on the development of that specific engine and she knows about the process of burning hydrocarbons from fuel in a pressurized and heated container, she has no relevance when her word goes against the manual which was written by the engineers directly responsible for these design choices.

Your mom has no idea what octane is. Higher octane has no benefit if the engine doesn't require it.

Unless your mom is an engineer and involved with the development of the Toyota, you should obviously go with what is stated in the owner's manual.

Go by the manual, but never use lower octane than that. They have some 85 octane in Colorado at the higher elevations, but I'll tell you from first hand that stuff cuts your power seriously and burns up fast. Never use it.