Welcome to ASRAnyone know what Im talking about? and have experience with both speakers?
I think i know what you are talking about and what the remedy is. You won't like it.
First, i have the Edifier r1280t, a variant of yours. It too has a 3.5" woofer.
The woofer is simply too small. There seems to be a minimum size to sound good in a regular room at a few meters, and our speakers just don't have that.
I have a pair of Yamaha HS7 that sound vastly different. They have a 6.5" woofer, i believe that is the main difference. Yes, they have more watts and the amp likely has a better SINAD, but i don't think that is what differentiates them. It's their size and woofer area.
What is there to do? I think it's best to use the Edifier M4 in the near field with a computer or something like it, and get proper speakers for your mother. I bought the Yamaha HS7 for 300€ a pair used, maybe you get another speaker with a properly sized enclosure and woofer for less. I think 6.5" is the minimum for me now. There are exceptions, like the ones from Genelec and Neumann, but these are a bit beyond the budget of regular folk like us.
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