I wouldn't bother trying to cover him with the umbrella. He's gotta learn the faster he performs the sooner he can get warm and dry. I wouldn't stop him from being under the umbrella - I just wouldn't go out of my way to hold it over him.
I think you give him a bit too much time wandering unsupervised - too much opportunity for accidents if you're busy.
It is also good to get him used to being in the crate - when you are home as well as when you're out.
You don't want him locked up for hours and hours, a play pen might be a good option.
Something like one of these - you can feed him in there.
Dog Exercise & Play Pens for Dog in Australia | Vebopet.com.au
Feeding in the crate is good to help him have good feelings about being in there or to protect him from other family members but if he already loves it in there and it's more convenient to feed somewhere easier to clean that's ok too.
I'm a little bit fuzzy about your routine leading up to kinder but I think something like
45 minutes before leaving for kinder - put him in the crate for 30 minutes - then take him out for the 15 minutes before kinder - to potty, then put him back while you are doing the kinder run.
After your errands let him out for a potty and maybe a 10 minute play, eg while you have a coffee break and can watch him - and when you're done - potty again (just in case) and back in the crate until you're ready again. Set cake timers for every 2 hours or when ever you want to let him out again.
When things are less hectic and you can pay more attention to what he's doing - you can let him run around with you more.
No food after 6:30pm. I'm not sure about restricting water but if the dry food stops at 6:30pm, the dog is less inclined to want water after about 7:30pm ish.
Can you get OH to take him out around 10:30pm for potty (even if it's raining - put him on the wet grass)? Otherwise you need to set an alarm and take him out. Try that for a week and then push the alarm time to an hour later.
I guess that will be about as much fun as having a small human baby again but it's better to work through the pain for a couple of weeks than have a life time of puppy messes... Note - it's always possible to retrain potty if it goes wrong but it always means going back to basics and starting over.