hi Vadim-
Sorry to hear that you're having trouble with AUTDv1. AUTDv1 is the SMS-based solution, and troubleshooting info can be found here:
http://support.microsoft.com/default.aspx?scid=kb;en-us;822176
AUTDv2 (or, "Direct Push", as we now call it) has several distinct differences and improvements over AUTDv1 that I mentioned in my blog. Among those are that it is entirely based on data connections. So the behavior you describe, where scheduled sync works
but AUTD does not, cannot occur with Direct Push -- that is, if scheduled sync works, Direct Push must, too, and vice versa.
Further, it requires no additional setup on the device. Once you provision ActiveSync on the device for doing scheduled sync, that device has all it needs to establish a Direct Push session, too.
Last, when SP2 is released, I hope you'll give it a shot and let us know how it goes. I suspect that the experience will be much more smooth than what you've seen with AUTDv1.
Best,
Sami