What I imagine is that basically they would meet at some point when they're a little younger and would just be completely unable to stand each other at first; and they would have rap battles about whose father is better and which one of them is more talented and basically just annoy the heck out of each other...and then as they got older they would eventually become friends and then more than friends, and of course Alex would be like "NO THIS IS NOT HAPPENING" and Burr would be like "GET THE HECK AWAY FROM MY DAUGHTER, YOU EVIL HAMILTON SPAWN" and it would turn into a sort of Romeo and Juliet thing and they would sneak out to see each other in secret and FOR THE SAKE OF THIS WHOLE IDEA, LET'S JUST PRETEND THAT NEITHER OF THEM DIES and wow now I'm rambling I'm sorry I am trash I'm just gonna go sit in a corner and obsess over this some more okay byeeeeee

^ wow I basically came up with an entire plot line there

^ yes