The 'wallet import format' (WIF) is a standardized way of encoding a private key so that other wallets can recognize it. You could use it to import the private key to your node's wallet, and then sign and send the transaction from there, but I think thats different than what you want to do: keep the private keys on the mobile, but broadcast signed transactions from your node.
bitcoin-cli command you'll want is
sendrawtransaction, but in order to make this work you'll need to get a signed raw transaction hex to use as input. So you'll need a mobile wallet that can provide you with the signed raw transaction, and do so without broadcasting it to the network.
bitcoin-cli help sendrawtransaction for more detail on the command.
As another option, you could use a mobile wallet which allows you to manually connect to the desired node. This would accomplish a similar result.