(For training purposes) Are there any openings with rook pawns that are more effective than others (and if so, what are they)? (Originally I hoped a lengthy prologue would not be needed here, but some of the answers and comments have led me to write one so that the purpose of the question is clear, thus this is now much longer.)

When my child was around six or seven years old, I taught them the rules of the game and basic principles of opening play. At the time, chess didn't seem to hold a lot of interest. However, move forward a few years, and playing with school mates after classes were over led to an interest in the game. Quickly the kid rose above the novices at school and could even beat the teacher. Games between the two of us became competitive, even though I usually - but not always - win. The kid played a few tournaments: in the first 8 the kid had positive records in all but one, which was an open where all opponents were adults with ratings 300 to 500 points better with one exception - an unrated player. There are three trophies on a shelf from these tournaments, including first place from the beginners section of our state scholastic championship. Along the way, we signed up for a year of chess instruction from professional instructors. Also, the kid watches videos online about all aspects of the game and has worked through at least one well respected chess book. It is clear that the kid has a decent understanding of opening principles for someone at this level.

At tournament nine the kid had a bad day. One game in particular stands out: The opposing player opened with 1) a4 ... 2) h4 (or something similar, I don't have the scoresheet). Ultimately, the other kid won the game because my kid didn't know how to respond and got rattled. In some ways this isn't surprising, as any time any person encounters an unusual situation they can get confused and make poor choices. 

Don't get me wrong, I certainly want my youngster to learn good chess principles. I don't want to play first moves like a4, h4, a5 or h5, in serious games, nor do I want the kid to do so (at all).  However, I've seen other games opened this way by players just learning the game (or using strange openings to confuse their opponents). In order to boost my kid's confidence and provide experience against games like this, I want to (occasionally) play openings at home that may be seen in games at this level. I don't expect to win these games, but that isn't the point: The point is to provide an experience that will benefit the psychological aspects of my kid's game if another player tries a similar opening in the future. Thus, I'm seeking some guidance on strange openings like 1) a4 or 1) h4, that I could at home play against my kid to help prepare for future tournaments.
Learning good chess principles and playing against clearly dubious openings like 1. a4 or 1. h4 are not mutually exclusive.  In fact, following solid opening principles is the best way to counter weak openings like this.

The moves 1. a4 and 1. h4 are both poor because they do not follow any of the opening principles.  Namely, they do not help control the center, they do not develop or prepare to develop any pieces and they actually reduce the king's options as to which side to castle on by weakening the pawn cover on one side of the board.  

To counter such a move, you should simply play normal opening moves.  1... e5 or d5 is a good start.  If white allows it, you can take over the center by advancing the other central pawn two squares as well.  Then simply continue by developing the minor pieces and castling the king to safety.  At this point you will have a large lead in development if white has continued making many foolish pawn moves (which is likely against the type of players who open with 1. a4 or 1. h4) and should be able to make life miserable for the opponent.