Technically, no. But, as a DM, I think B is best bet, here's why (in order of favored to least favored options).
(b) Retraining (Swap)
This seams like the best option RAW and RAI. This is essentially creating a clone of the character who happened to study a different school of magic, who is instantly swapped with their doppelganger. You would end up with a RAW lvl 2 wizard who is just of the other school. Story wise, you might want to come up with a reason for why they lost Spell Sculpt and gained Arcane Ward, but that could be as simple as "the arcane knowledge takes up too much head space to know both", something to do with the weave not being that strong, or Ioun not liking it... or whatever.
(d) Not Allow It, and new Character (Just Say No)
This is likely the most RAW answer, but it is also the least fun and could make your player quit (but not likely unless other things are going on). In the real world at the table, the point of the game is be fun.
If the player constantly requests these kinds of large changes, the answer is no; but if they made a mistake early on and they new to the game, and this is the first request there is no harm in working with them. I would make it clear this is a one time deal and you're not bending the whole world to their whim.
(c) Forgetting and Starting Fresh (Penalty for Changing)
This is too steep a penalty that will continually have your wizard at a huge disadvantage. It is very likely a penalty that steep would make your player quit, and the point of the game is be fun. I wouldn't do it.
(a) Multiclassing the Same Class (Gaining Both)
Choosing multiple wizards schools can causes problems because different schools strengths are at different levels. Portent from divination is is really strong and you get it at level 2, as is the arcane ward and it also starts at level 2. That means you could end up with a really OP character that can change rolls and have extra resilience through the arcane ward at the same time, which is strictly better than any cross-class multiclass. Which is why it is forbidden as we see in this question: Can you multiclass the same class twice for different class features?
This is clearly the farthest from RAW or RAI, and would likely ruin your game experience for more than just the wizard character. They would be gaining more power than the rest of the players.
Whatever you do
You are the DM. The rules are there as a guide, not as a law. If you and your player agree on a way forward that isn't exactly RAW or RAI, but it doesn't upset balance to the game, do it. If it doesn't work out balance wise, tweak it.
These sorts of changes can drive the story. Maybe to this change requires some action on the part of the player. Find an item or book, help an archmage, or some other quest to gain the reward of retraining.