Is the mother considered sinful for not cleaning her children from urine, even though she cleans them from feces, and she fears being held accountable for that in the future?

There is no sin in not washing away or wiping the urine of an infant boy due to his lack of accountability, and this does not invalidate worship. However, it should be cleaned of filth. He must be raised to perform Istinja (definition)' (cleansing after relieving oneself) and avoid impurities upon reaching the age of discernment.