Overwhelmed nanny in need of advice?

I am a nanny for two children. The parents spend very little time with their kids-they are in preschool or with nannies every day of the week. Lately their 1 and 4 year olds have both been having huge meltdowns and tantrums every time they don't get their way. The 1 year old will scream for 20 minutes at the top of his lungs over not getting his way such as I didn't let him climb up the stairs when he wanted to. I'm starting to feel really overwhelmed. I try not to show attention when they do that or try to redirect but it's not working. They are incredibly strong willed children. I love them to pieces but I'm starting to really dislike my job. I work long hours almost every day of the week.

Any advice on how to cope with this phase? Or do you think I'm just not cut out for this type of work? If I tell the mom I'm feeling overwhelmed, I might lose my job. I never realized how stressful it could be to listen to children cry so much. I've been a nanny for years but never experienced this difficult of a situation.
Added (1). The parents also make my job harder. If I'm giving a time out to a child, they will intervene during the trantrum to give the child an Ipad and a snack… I feel like the 4 year old needs discipline but I'm the only one giving it to her.

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