No, send the ITIN applications together with the tax return -- one package with all the documents at the same time. The IRS will issue the ITINs and then will process the amended return. The ITINs will likely take a few weeks and then the amended return will probably take 16-20 weeks to process, amended returns are really slow.
That's why you also need to send a copy of the amended return along with a letter of explanation to the office that sent the notice. You need to let them know what you are doing, and that you are in the process of correcting your mistake, but the timing is up to the IRS. (Maybe include a copy of your proof of mailing too.)
Normally, when you want to fix an issue from a letter by amending, you would send the amended return directly to the office that sent the notice, instead of the normal address. The problem here is the added complication of the ITINs. So I think the best course is to send the entire package off to Austin Tx, tax return and applications together. (You need to include the tax return because the IRS won't issue an ITIN without proof of a financial connection to the US, and your marriage and joint tax return is what creates the financial connection.)
You could possibly try to work through a taxpayer acceptance center or acceptance agent. But I think the mail will be ok. But you need to send an explanation and a copy of everything you are doing to the office that sent the notice so they can pause their action until the amended return is processed and they can see if the 1095 matches the new information.
You may want to see a tax professional if you are still worried about the process.
