I can see both sides of the story. First of all, you want a safe place for your kids to play ball and so on. On the other hand, when did the street become a playground?
Twice in my neighborhood over the past month I have had to spend money because kids are playing in the street. The first time I was driving the minivan, slowed for some kids who were playing baseball in the streets and had my window broken by a line drive. Three weeks later I was riding my motorcycle and some kids had moved their basketball hoop out the edge of the driveway and were using the street as the court. Because of the way the cars were parked, if you were around the basket, you couldn't see me coming. Because of the music they had blasting and their yelling, you couldn't hear me. (I have a fairly quit bike) Five of the kids moved out of the way...the sixth was under the basket. He turned and threw the basketball just as I passed and hit me in the head, nearly knocking me off the bike. I managed to save it, and not laying it down, but because of the way I saved it, I sprained my ankle.
Now, when it comes to pedestrians verus cars on the road, who has the right of way? Well, Texas law says:
§ 552.003. PEDESTRIAN RIGHT-OF-WAY AT CROSSWALK. (a) The
operator of a vehicle shall yield the right-of-way to a pedestrian
crossing a roadway in a crosswalk if:
(1) no traffic control signal is in place or in operation; and
(2) the pedestrian is:
(A) on the half of the roadway in which the vehicle is traveling; or
(B) approaching so closely from the opposite half of the roadway as to be in danger.
(b) Notwithstanding Subsection (a), a pedestrian may not suddenly leave a curb or other place of safety and proceed into a crosswalk in the path of a vehicle so close that it is impossible for the vehicle operator to yield.
(c) The operator of a vehicle approaching from the rear of a vehicle that is stopped at a crosswalk to permit a pedestrian to cross a roadway may not pass the stopped vehicle.
§ 552.005. CROSSING AT POINT OTHER THAN CROSSWALK. (a) A
pedestrian shall yield the right-of-way to a vehicle on the highway
if crossing a roadway at a place:
(1) other than in a marked crosswalk or in an unmarked
crosswalk at an intersection; or
(2) where a pedestrian tunnel or overhead pedestrian
crossing has been provided.
(b) Between adjacent intersections at which traffic control
signals are in operation, a pedestrian may cross only in a marked
crosswalk.
(c) A pedestrian may cross a roadway intersection
diagonally only if and in the manner authorized by a traffic control device.
(There's more here, which supports you, and also supports them: http://law.onecle.com/texas/transportation/chapter552.html)
So what do I think? You're both wrong. Don't let your kids play in the road, and if you do, be prepared for those who are frustrated that you let them play there, instead of in the backyard. And yes, I think you should write them a little note. Just explain why you, and your children, enjoy playing out there and ask that they not come barrelling through there. Tell them in return, you'll be more courteous when you see them coming and move immediately, and if you hear them coming, you'll make sure the children hold their balls, etc so as not to have it come into the road in front of them.