In case anyone have that bug where both Laura and the Pizza and the birthday event triggers at the same time, i had the same problem and ended up finding a way to solve it, so i might as well share what i did:
If you continue on the birthday stuff you will get locked. You can't access your bedroom, and even if you do with the bugfixer and you send Laura interacting with the home entrance door won't trigger the scene.
So what you can do to fix this; luckily game asks you to save just when the birthday event triggers, so use this save (and remember what day it is).
When you get teleported to mall to buy Sarah a gift, use bugfixer to tp back to your bedroom. From here you can continue on with the pizza stuff without problems.
You then play Laura a bit where you have to go to Kitchen, Amy's room (which reminds me she's not even there for the birthday, did beggar forgot her?), Sarah's room, lucy's room, living room and bank. Now the pizza stuff is done. Carefull, going to Laura's room when you play Laura triggers the Sarah/Laura Threesome immediately.
To get back to birthday event, i don't know if it's necessary but i cheated out the day and time to what it was before the pizza stuff (should be 11:00 am of whatever day you were on) and teleported back to the mall. From here you can buy Sarah's gift and proceed the birthday event normally.