How do I convince my parents to return my savings to me?

Start from partial the full control of your own finances.

I'm in a similiar situation with you. I'm in my 20s and my dad bought some investment policies for me and he still refuses to let me manage that. I guess they want the best for us in the meantime, built up your own finances and not "hope" or "rely" on that.

Your mum actually wants the best for your money like you do, just that the older generation are usually more conservative than us young souls. They are afraid to see you release it all in the scary markets they've never been into.

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The most straightforward way will be to explain to her step by step what you will be doing to show her you are not being careless. But knowing most hard-headed parents (speaking from experience), they will either just release a little more of your savings to you or none at all.

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If they reject your proposal, it's totally fine. After all, the money will still yours in the end. The best way to deal with it is to treat it as a build-up of emergency fund that you can bring with you into your adulthood. Right off the bat, you will have an emergency fund ready to go and you will worry less about building it up when you start working a few years down the road. Then you can allocate even more capital to maybe a housing fund or even volunatrily contribute more to CPF. It all boils down to perspective.

Your mum wants to safeguard your money. She is worried you may do something reckless with it, even as you have reached adulthood.

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If you would like to maximise your returns on the remaining 87.5%, persuade your mum to let you put those in fixed deposits for now.