If First node in the private blockchain deploys the contract and second node in the network wants to request data from that contract, then how the second node will send request to the smart contract?
Contracts work the same way as they do in public ethereum networks.
Once your contract deployment transaction is mined into a block, any node on the network can broadcast a transaction that interacts with that contract by making calls to its address. The address can be found in the tx receipt that deployed the contract.
Note that for read-only calls, the node making the call must have synced past the block that deploys the contract. Similarly, for writing to it, the results of the write transaction (such as logs) will only be available once the write tx has been mined.