[blazey]

I don't have my own children but I look after my own brother and sister a lot and also work with kids during summer, and I always operate the rule that if they are fair with me then I will be fair with them.

Instead of being patronising, sit them both down and explain that you want to enjoy them being home from school for the summer, and that of course means no screaming, because nobody enjoys screaming.
Explain that you want to spend time with them both together and individually and you will treat them both equally.

I always sit everyone down and ask everyone individually how they are feeling, and that includes me. Then everybody has an opportunity to say how they are feeling and if they hear bad things about themselves from people watching, for example if your son said that he hates seeing you sad because of your daughter, she'd hopefully feel a bit ashamed and apologise to everyone.

Then you can all have a big hug and get on with the day!

Of course, I don't have to do this often with my brother and sister, but it works with kids on courses, particularly if you have one nightmare child and everyone says constructively that they need to calm down and have fun instead. It might not work, but it is an option and will at least help with the communication issues.

Either that or result in WWIII.