I won't ref bash but the decision depends largely on your understanding of the game and this situation. If you've played the game, it is clear that the covering defender is going to get back to cut her off (due to the attacking players' first touch not being great), so it's not DOGSO. If you haven't played the game and/or don't fully understand the situation, you perhaps just see an attacker running toward goal and likely give a red. Again, I'm not ref bashing (I was one for a long time). All of that said, it is open to interpretation and opinions will vary, as they always do in these situations. The sensible (and fair IMO) option? Give a yellow. Kicking the ball away for a potential 2nd yellow? Hardly, it goes about 5 yards but again, an overly officious referee might see it differently.
The "yeahhh" and "wooooo" reaction to the red card made me laugh, then cringe. I always wonder why parents 'cheer' yellow and red cards in youth soccer.