Only 15 days to go before due date for filing taxes expire. I need to apply for ITIN No for my spouse and kid. This can take 4-8 weeks. Can I submit a cheque with the amount due to IRS along with W7(ITIN) application (will IRS get back to me automatically with the refund) or do I need to pay my tax dues and submit W7 separately and then claim for a refund separetely?

If you will owe money if the ITINs are not approved, then send a check with the tax return that is equal to that tax owed. The IRS will refund it once they issue the ITINs and process the return.