That's been solved. Avoid them and shield your spacecraft...just like we did when we went to the moon. Even if we fly through them the radiation exposure is minimal due to how little time is spent there. You're been watching WAY too many youtube videos.
From VanAllen belts on Wikipedia:
The Apollo missions marked the first event where humans traveled through the Van Allen belts, which was one of several radiation hazards known by mission planners.[32] The astronauts had low exposure in the Van Allen belts due to the short period of time spent flying through them. Apollo flight trajectories bypassed the inner belts completely, passing through the thinner areas of the outer belts.[25][33]
DouglasKC,
Take it up with NASA. They produced the video.