Is the OP feeling okay?
Not sure how this isn't DOGSO, applying the laws of the game:
"Where a player denies the opposing team a goal or an obvious goal-scoring opportunity by a handball offence, the player is sent off wherever the offence occurs (except a goalkeeper within their penalty area)."
- distance between the offence and the goal = 20 yards
- general direction of the play = going towards goal
- likelihood of keeping or gaining control of the ball = the ball is potentially going straight in the goal so not required
- location and number of defenders = whilst 3 defenders, they are unlikely to get the ball if it is going in
The referee is having to make these considerations from the halfway line.
Most of all, in my opinion, the game
expects a red card in this situation. As a referee, you shouldn't have to mitigate for the goalkeeper's stupidity.