Is there a way to schedule when the Market updates my installed apps? Ideally I would like to run it late every night, that way I won't have to be bothered with them when I'm actually using the phone.
I'm not 100% sure but maybe tasker can do it. If it can't do it directly and if you are rooted, you can use tasker to kill Market except on night time. That way at night time Market will run and install your apps. At day time market will get killed and no installing of apps.
You can set the Market to only update apps when its connected to Wi-Fi. If you only ever connect your device to Wi-Fi at home, then this setting could do the trick for you?
Market -> Menu -> Settings -> Update over Wi-Fi only
It seems that the "Update over Wifi only" setting was only added to the Market app in v3.3.11. If your Market app is stuck on an older version then you can try to force an update by clearing the data on the Market app, or manually download and install an updated Market APK, as detailed in this previous question.
There is no perfect way to do this but there are other ways to 'control' the updates. You can disable auto-updating, or only via Wifi from settings. You could also force stop the Play store app and then later in the day when you are connected to Wifi and not using your device, you open the app again and it installs updates.