Perhaps another ending would work, but I doubt it would be better. Rather than Paul's mother practically drooling over the huge sum she's about to get, a sentimental writer may have had the mother toss it all aside and run to her poor son. The sister/daughter has been ignored; perhaps she could be brought into the picture to give us some sense of hope for the future of this family. In any case, for me there would have to be some sense of redemptive hope and change for the future in order to qualify as "sentimental." As it is, we have none.
jlcannad is right in pointing towards a greater, softer role for the mother in this story. Of course, I wouldn't change the ending, as it would completely change the theme and message of this powerful story, but a more sentimental story would involve a definite "softening" of the mother by the end of the story and her prioritising relationships over money. Greed, the key theme of the story, is what isolates her and prevents her from truly loving her children, and this is what drives Paul to ever greater excesses on his rocking horse. A more sentimental approach would make the mother realise what Paul is doing to himself sooner, enable her to live within her income and involve a "re-bonding" with her children, and especially Paul. Prizing relationships over money would definitely change the tale.
I'm going to assume you mean the literary sense of sentimental as in the 18th century writing where female protagonists are "guardians of spirituality and virtue." In this story, the mother, rather than being the spiritual center of the family, is well aware that "at the centre of her heart was a hard little place." The boy is the virtuous one who is willing to sacrifice in order to try and stop the whisperings that hurt both his mother and the entire family.
If this story were sentimental, I would expect the mother to either be the moral center of the family or to become the moral center. At the end of the story, her heart is not changed. The ending would also have to be more optimistic to fit into the sentimental genre. Right now, we can assume a pessimistic ending simply based on what we have seen. When the mother got the original monetary gift, she got a "cold, determined look" on her face and wasted even more money on things such as flowers and "iridescent cushions" while the whispering got even more desperate. Now that she has inherited sixteen times more money, the destructive nature of the mother's wastefulness is likely to just accelerate. So, the child is dead, there is little to no hope for moral improvement, and the woman is the center of this little disaster, despite the fact that she blames her husband for their lack of luck. All this would have to change before this could be called sentimental.