As far as I remember in order to prove negligence you have to prove some kind of intent. Below are the laws for bicycles in NY. Another thing is who owns the sidewalk? In certain states the sidewalk belongs to the city in others it belongs to the homeowner. Either way this is going to cost both parties money. A jury is going to have to find that the defendant was responsible by a preponderance of the evidence. It won't be easy because your dealing with a elderly lady vs a small child, it does help the defense that allegedly the death was not caused by the injuries due to the accident. Either way this is a very tragic story and really nobody wins.
(Sorry I had to post the entire statute because it wouldn't link up).
§ 1234. Riding on roadways, shoulders, bicycle or in-line skate lanes
and bicycle or in-line skate paths. (a) Upon all roadways, any bicycle
or in-line skate shall be driven either on a usable bicycle or in-line
skate lane or, if a usable bicycle or in-line skate lane has not been
provided, near the right-hand curb or edge of the roadway or upon a
usable right-hand shoulder in such a manner as to prevent undue
interference with the flow of traffic except when preparing for a left
turn or when reasonably necessary to avoid conditions that would make it
unsafe to continue along near the right-hand curb or edge. Conditions to
be taken into consideration include, but are not limited to, fixed or
moving objects, vehicles, bicycles, in-line skates, pedestrians,
animals, surface hazards or traffic lanes too narrow for a bicycle or
person on in-line skates and a vehicle to travel safely side-by-side
within the lane.
(b) Persons riding bicycles or skating or gliding on in-line skates
upon a roadway shall not ride more than two abreast. Persons riding
bicycles or skating or gliding on in-line skates upon a shoulder,
bicycle or in-line skate lane, or bicycle or in-line skates path,
intended for the use of bicycles or in-line skates may ride two or more
abreast if sufficient space is available, except that when passing a
vehicle, bicycle or person on in-line skates, or pedestrian, standing or
proceeding along such shoulder, lane or path, persons riding bicycles or
skating or gliding on in-line skates shall ride, skate, or glide single
file. Persons riding bicycles or skating or gliding on in-line skates
upon a roadway shall ride, skate, or glide single file when being
overtaken by a vehicle.
(c) Any person operating a bicycle or skating or gliding on in-line
skates who is entering the roadway from a private road, driveway, alley
or over a curb shall come to a full stop before entering the roadway.