brownhorse.... i seriously was you last year and the year before and it impacted my job tremendously. i was certain i did not have any options and felt that way (and did have limited options but there are always options) and the reality is that i COULD have come up with a better solution than depending on AH if i'd been willing to.
i did not want to ask friends and put them out or risk hearing no. i did not want to deal with the discomfort of possibly saying that i had to ask for help bc AH was unreliable.
i wish i'd done things differently. i let my career be impacted by AH bc i didn't want to accept that i'd have to start looking elsewhere for help and didn't want to accept that i couldn't do it all myself.
i won't lie- it WILL impact your job. but it doesn't have to. ideas: ask a neighbor if they are willing to help in a pinch, call a friend who you are certain doesn't want to take a sick kid and ask if in an emergency they will. if AH can not be relied on (i get that you have to call early-- me too) then have a different plan that doesn't involve him at all. ask work about their employee assistance program and maybe through that you can get info about emergency childcare options...
i didn't ask people for help for many of the reasons you list and you know what? once i did ask bc i wished i'd asked sooner. people are willing to help. but you have to ask. i wished that someone would just offer or a comfortable and easier solution would present itself but it didn't. i had to struggle and figure it out but i found when i started to look and ask for help that there actually WAS a lot out there...
i am so sorry for all you are going through. i literally know exactly what you are experiencing and feel so terribly for you...