The hacker can't get your private key because on blockchain's wallet they don't give out private keys anymore unless you've been using their wallet since the old version and your old addresses was imported.
This is something new for me. Wasn't it good before? Everyone should have own their own private keys/seed. I can not remember when was the last time I used blockchain wallet but as a newbie it was very handy for me long ago.
I hate Coinbase by the way.
My BTC address: 1FgpbfQ8nVMS523Btnyv3rxhF7YxtiEdr7
Created with blockchain.com 2 years ago.
Funds received more than a year ago. It was safe during all period, I always paid much attention to security.
The loss was realized yesterday, Aug 27, 2019 morning, I turned on computer, checked my e-mail as usual (again there was no notification from blockchain.com),
before that, the computer was turned off all night.
2019-08-27 07:03:08
Amount: 0.035 BTC (350 USD)
Transaction ID: 4d412c58ab3dba8a138557e41e9ace1c8b36ee3d44107a930c8f31f0198d2b93
Recipient address: 1PdXxtu8Laq773RXT5q5pp6qtaG3HvSw2r
Your information was compromised for sure. I am afraid to tell you that, there are nothing much you can do now. This is the reason I do not use online hot wallets even I do not use a standard wallet for large percentage of my Bitcoins. I use 2/2 multiSig wallet.
My suggestion is that - consider it as a lesson and move on. Sorry for your lose.