sign.js

var bip39 = require('bip39');
var bitcoin = require('bitcoinjs-lib');
var Wallet = {};

// FILL IN: REDEEM_SCRIPT, MNEMONIC1, PASSPHRASE, MNEMONIC2, TARGET_ADDRESS, TXID, VALUE


// build like here: https://github.com/blocktrail/blocktrail-sdk-nodejs/blob/ff4bde6983385f5adff3a89e10959ddc323e4160/lib/wallet_sweeper.js#L228
var redeemScript = new Buffer('REDEEM_SCRIPT', 'hex');

var primaryPrivateKeyMaster = bitcoin.HDNode.fromSeedBuffer(bip39.mnemonicToSeed('MNEMONIC1', 'PASSPHRASE'));
var backupPrivateKeyMaster = bitcoin.HDNode.fromSeedBuffer(bip39.mnemonicToSeed('MNEMONIC2'));

// change path: https://github.com/blocktrail/blocktrail-sdk-nodejs/blob/ff4bde6983385f5adff3a89e10959ddc323e4160/lib/wallet_sweeper.js#L252
var primaryPrivateKey = deriveByPath(primaryPrivateKeyMaster, 'M/0\'/0/0'.replace("M", "m"), "m");
var backupPrivateKey = deriveByPath(backupPrivateKeyMaster, 'M/0\'/0/0'.replace("M", "m").replace("'", ""), "m");

var keyPairs = [primaryPrivateKey.keyPair, backupPrivateKey.keyPair];
var pubKeys = keyPairs.map(function (x) { return x.getPublicKeyBuffer() });
console.log(pubKeys);

var txb = new bitcoin.TransactionBuilder();
var targetAddress = 'TARGET_ADDRESS';
var unspent = {
    txId: 'TXID',
    vout: 0,
    value: VALUE
};
txb.addInput(unspent.txId, unspent.vout);
txb.addOutput(targetAddress, unspent.value-10000);

txb.sign(0, backupPrivateKey.keyPair, redeemScript);
txb.sign(0, primaryPrivateKey.keyPair, redeemScript);
var tx = txb.build();
console.log(tx.toHex());

function deriveByPath (hdKey, path, keyPath) {
    keyPath = keyPath || (!!hdKey.privKey ? "m" : "M");

    if (path[0].toLowerCase() !== "m" || keyPath[0].toLowerCase() !== "m") {
        throw new blocktrail.KeyPathError("Wallet.deriveByPath only works with absolute paths. (" + path + ", " + keyPath + ")");
    }

    if (path[0] === "m" && keyPath[0] === "M") {
        throw new blocktrail.KeyPathError("Wallet.deriveByPath can't derive private path from public parent. (" + path + ", " + keyPath + ")");
    }

    // if the desired path is public while the input is private
    var toPublic = path[0] === "M" && keyPath[0] === "m";
    if (toPublic) {
        // derive the private path, convert to public when returning
        path[0] = "m";
    }

    // keyPath should be the parent parent of path
    if (path.toLowerCase().indexOf(keyPath.toLowerCase()) !== 0) {
        throw new blocktrail.KeyPathError("Wallet.derivePath requires path (" + path + ") to be a child of keyPath (" + keyPath + ")");
    }

    // remove the part of the path we already have
    path = path.substr(keyPath.length);

    // iterate over the chunks and derive
    var newKey = hdKey;
    path.replace(/^\//, "").split("/").forEach(function(chunk) {
        if (!chunk) {
            return;
        }

        if (chunk.indexOf("'") !== -1) {
            chunk = parseInt(chunk.replace("'", ""), 10) + bitcoin.HDNode.HIGHEST_BIT;
        }

        newKey = newKey.derive(chunk);
    });

    if (toPublic) {
        return newKey.neutered();
    } else {
        return newKey;
    }
};