I'll throw my 2 cents in the hat, as I have found value across the board of ideas here.
Due to the many issues outlined above, I am usually involved in my daughter's warmup one way or another. Whether I am asked by the coach or whether we come 30-45 minutes before the team (her choice) in order to get her rolling. I have experience as a club coach, keeper coach, and ref, so I feel I have a little to offer her, but I also don't want to step on the coach's toes, so we do discuss with them prior to and if they have issue or don't want it, then I have no problem stepping back.
My philosophy for the warmup is based around confidence and rhythm. All drills are a buildup. If we're working catching, we start with nice tight catches, then work our way out to moderate stretch catch, then eventually we end it with just outside a catch range and it turns into a push. If at all the flow of this is broken, we take a step back and rebuild. So many times when I watch the warmup of keepers, I see these difficult to save balls that had no buildup to establish the player's range. By no means am I suggesting this be a cakewalk, but from my experience, you have to build out the range, not just jump in with tough shots and wonder why they aren't stopping them.
Throughout, we do move back and forth from hands, feet, in-air, diving, etc. We have a specific 3 in a row dive sequence that is our gauge for where she is in the warmup process. We randomly run this sequence throughout and once that gauge hits and she is confident, we stop and just move onto goal kicks and punts.
The next phase is usually the one that most parents, players, and keeper coaches hate, which is the team shooting. Unfortunately, it's a necessary evil for the field players, so I have always advised my kid and players that I've worked with to approach it as follows -
The drill is not for them, it is for the field players and is the equivalent of their confidence and rhythm building. So, instead of worrying about making saves during this time, focus on establishing the proper angle before the shot, feet ready, and body balanced.
When the shot is taken, evaluate whether you think you were in the right spot, could you dive well from your spot, would you have made the save? I then suggest that they take every 4th or 5th shot (depending on pace of drill, players involved, and number of keepers) and on those shots is where they go full circle - Angle, feet, balance, AND attempt to make the save. From the feedback I've received from players, they find that this is a bit better and keeps their confidence where it needs to be, gives them opportunities for full action saves, and allows the field players to get what they need out of it.
Great post. Funny how many keeper parents go all in (I've worn all 3 hats too, though prob. not with your experience). Question: so if the coach has an issue with it, who does your daughter's warmups (I'm assuming in that case the coach steps up and either does it himself or the assistant does it)? Would love to hear more about your 3 in a row dive sequence. Also, do you cover extension diving....I've seen a split whether the extension dive in the air should be a part of the warmup...MLS players usually do it, but some coaches think for youth keepers (especially intermediates) it's a way to risk injury and/or shatter confidence so they stick to easier saves nearer to the set position in the philosophy now is not the time to challenge the keeper?