It seems that you don't understand the basics of the blockchain... It is, by design, a completely public ledger, that records "transfer of value" from one ore more public key(s) to one or more other public key(s).
To be able to transfer value from any given public key... you need to be able to sign a transaction. The only way to successfully generate a valid signature is with the private key that matches the public key. The asymmetric cryptographic properties of a signed transaction allow anyone to validate that the signature provided matches the public key, thus proving that the person has access to the private key and is therefore the "owner"... WITHOUT needing to know the private key.
As value is moved from one address to another, you can follow the chain of transactions... from AddressA -> AddressB -> AddressC etc etc... You can see that the value moved from A to C (via B)
People use mixers, so they can then do this:
AddressA -> AddressB -> MixingServiceAddressX
...
chain broken ...
MixingServiceAddressY -> AddressC
The idea is to "break the chain" such that AddressA can no longer be linked through to AddressC... With no direct link between MixingServiceAddressX and MixingServiceAddressY, you can't (easily) link A to C...
All of the convoluted things you are attempting (or think that you need to do) are unnecessary if you put the coins into a service like ChipMixer... it takes care of breaking the chain so that addresses used PRIOR to the coins being sent to the mixing service are no longer directly linked to addresses used AFTER the coins are withdrawn from the mixing service.
In ChipMixer's case, the majority of the private keys are actually funded well BEFORE you even send coins to the mixing service... which makes it even harder to track the flow. As you coins are effectively time travelling

NOTE: Mixing services are not 100% effective... Advanced analytics companies exist that can still determine movement through mixers to a certain degree. If you REALLY need full anonymity, better to use a privacy focused blockchain like Monero etc.