Assuming that everyone switches to one of the chains and ditches the other one, your money wouldn't be halved by definition because the other chain becomes defunct because no-one is using it at all.
Wrong assumption.
There are always dissidents, even if the top mining farms agree on hardfork and say 3% of the network doesn't.
The small miners will mine the old chain, because the difficulty will be low there once the big guys get out, and then slowly the miners will come back there because the diffuculty drop incentive as more and more support goes there.
Eventually it will settle at 50-50%, the supply of bitcoin doubles, and your
money will be worth half as it was previously. Enjoy that...
Mining difficulty will not be low. I think that is your fundamental flaw here.
With 3% hash power it will take forever to mine a block.
You can trade all you want on that chain. You will never receive your "bitcoin".