Help with tricky remote admin situation

Fun Challenge for the experienced Systems Administrator
I am a tech guy in a small startup firm. I know the basics of working on computers, troubleshooting networks, and updating software.

We are a market research firm that has no office, so we end up moving 20+ laptops around with us from job site to job site. These laptops need to be updated with windows updates and other programs (web browser updates, java, flash, etc).

I need to setup some sort of remote administration system to manage all of these laptops at once, so I don't have to manually update each one-by-one.

Heres the issue, we don't have a dedicated office, so these laptops are never online in the same place consistently. Networks vary from wired (easier) to wireless (harder).

Fortunately, they are almost always online in the same room on the same wire/wireless setup.

What is the best program suite to do the following:

Remote program/software update for everything from windows updates to java, flash, and individual .exe for specialty programs

Remote desktop (like Windows Remote Desktop) that is invisible, so we can see what the user is doing but they don't know that we're watching (to make sure our respondents aren't doing things they aren't supposed to)

Changing settings like toggling Windows Defender on/off on all machines, changing browser settings

File transfer between computers (from a 'controller' laptop to the others and vice versa)

Additionally, I've tried accessing other laptops using our workgroup (I can get them visible to a workgroup) but I can't get through, it says access denied and that I should ask a systems admin if I have permissions. I am not sure how to create a network/worgroup user profile that will give an administrator laptop (mine) access to each surveyor laptop (each of the 20)