Say I am building a transaction in private:

1. Input 1 is signed with SIGHASH_SINGLE ( | SIGHASH_ANYONECANPAY)
2. Input 2 is signed with SIGHASH_NONE | SIGHASH_ANYONECANPAY

SIGHASH_NONE implies that Input 2 will only spend if Input 1 is included in the transaction. Am I able to communicate this privately-signed transaction in such a way that Input 1 is also locked on the condition that Input 2 is included?

For example, I send this partially-signed transaction, with both signatures, to a person I do not trust.

Are they able to spend Input 1 in another transaction without Input 2 included?