hi dad! welcome to @motherhood, is so awesome to read a real account of your experience, is totally normal for kids specially toddlers not to sleep even with their mom by their side believe me it takes me hours to put to sleep mine.

As an advice for those tantrums again totally normal since toddlers and young kids in general dont know how to control yet their emotions, i found that taking myself a deep breath and try not to pay attention to what people my be thinking when he does that helps me calm down and not scream at him so much lol once im calm i can try and calm my kid down.

What i do is i get down to his level and ask him for a hug, this helps calm the crying when he is more calm i try explain the reasoning of why i need him to do what he doesnt want to do, like going or not buying something or whatever it is that is causing him to be so upset. my kid is only 2years and he may not understand fully somethings but i do feel like talking to him in a calm voice while i hug him helps a LOT. Hopefully this helps you a bit with your crying kid.

oh by the way I find that to help me put to sleep the kid turning all lights out incluing his night light helps a LOT! i start to talk to him in a soft voice and just holding him tight in a hug and he will eventually fall sleep.

so i guess my advice for dealing with your kids is just hug them out it helps a LOT.

ps: you should be careful with the pics you share online of your kids, your baby girl is still young but there are a bunch of creeps out there so i suggest when she is not wearing a tshirt to put an emoji over her body to cover her.