My grandmother is completely mobile and uses the bathroom unassisted. Problem is she sometimes makes a mess on the floor when urinating. I think she either doesn't sit far enough back or she gets up before she is done and the urine leaks out in between the toilet and the toilet seat. Is there a product out there that eliminates this gap or maybe a differently designed toilet seat? She doesn't need a seat riser as she can easily get up from the toilet on her own.
I would get a TIMER and a PADDED seat. I don't know how big your mother is but it can get VERY uncomfortable if she is thin. Also... get a TIMER... put it on for two minutes, and see if that helps. I'm not sure what 'gap' you are talking about, but a padded seat may help "keep her seated" until her business is done.
Then I would add a NON-SLIP bathmat that can be easily put in the wash to prevent messes AND to prevent any possible slips.
I do hope this helps, or someone else can their wisdom to help you!