Well then as I understand you will not be using a split key generation, since third parties will have the customers private key, which is kind of ridiculous. You might as well just make a online wallet with vanity address feature, instead of giving users false hope that only they can use that address. Third party here will have access to all the bitcoins forever and since customers payed money to have that address, there would be no sense in moving those coins to a better address. You might as well make a vanity address proxy service, where you pass along funds sent to those addresses.
Since the third party will have the private key anyway, you might as well make a online wallet without the option of exporting the private key to the customer and just generate all the vanity addresses from the same private key and keep it secret from all the customers. This would have the same security and save a lot of processing power.
No, you misunderstood!
We will use generation of vanity addresses using split-keys, but the partial public key for generation will be provided not by the customer, but by a third party. The full private key for the vanity address can be obtained using the partial private key of the third party and the partial private key of service, that generated the vanity address. It's clear that these 2 partial private keys will eventually be received only by the customer and no one else.