First of all the separation anxiety I've experienced in a couple of rescue bullies doesn't usually just mean looking and feeling down and depressed. It means some serious shredding and destruction of anything near the bully. So that's the good news!!!!! I dont' think Mocha has separation anxiety, cos that's REALLY difficult to deal with and to treat.
Scared of fireworks is something common ..... and to be honest I don't blame them. I don't really like fireworks.
Being joyful at you returning is normal. The vomiting not so much ... so I would say right now it's a coincidence and that hopefully the next time you have to go away that she will sulk BIG TIME and maybe pout a bit. You may even get some stink eye on your return before the joyful forgiveness.
If she throws up everytime you go away .. it's unusual and that may need more help.