Personally, I would play it a bit differently.

First, you have zero risk since there's a 24-hour refund policy. So I wouldn't hassle with the holding of a ticket, then going to use the other.

Next, if you want them both on one record, UA does have this functionality and is able to pull miles from respective accounts while keeping you both on one record (CO systems are not able to do this). But, with UA you will need to call to do this. If being on the same record is something you would like, you may want to consider moving the miles to your linked UA accounts and paying the call center fee to UA to have them make the booking.

That aside, if using co.com, I would search for two (2) award tickets on the flights you want, verify there's space all the way through for two (2) and it prices correctly. Then start over, and login for each of you on (2) computers or two (2) browsers on the same computer (e.g., one in IE, one in Firefox). That will give you two sessions. Build them and pay at the same time, and presuming the 2 seats are still there, they will confirm.

And again, if anything barfs, then you can always invoke the 24-hour refund.