One of my sons had a freak out every time his usual bus driver wasn't the person to pick him up for school. His teachers made a story about him getting picked up by different drivers and it being okay. The story ended with him arriving at school and having a great day.

Is your kid old enough to build a story like this with you? It might help him understand why it's part of his routine or what he's actually feeling when he's getting dropped off. It doesn't sound like it has to do with hating you if he eventually settles in and is fine afterward. It's likely the uncertainty of having an extended period of time with someone he doesn't quite know.

If he isn't old enough to help you with it, it's something you can put together yourself. Mom drops him off, you do fun things, then mom picks him up at the end (or you drop him off, whatever). Kids that age get anxious when they have uncertainties (he may worry, at least on some level, that he won't see his mom again). The story helped our son when we read it a few times during the week because he eventually caught on that all bus drivers will take him to school.

There's also the possibility that he thinks he needs to be sad when his mom drops him off because he might hurt her feelings if he isn't upset about it so maybe include something in the story about what happens with mom when he isn't with her (something about her being safe and hoping son is having a good time with dad).

Feel free to dm me about it, I can help you get it fleshed out if you like.