Should I re-do my entries? Should I file separately? My joint application with my spouse said over $4k in our refund… then I added my new w-2 and it changed to owing $382

That was normal.

WHY DID MY REFUND GO DOWN WHEN I ADDED ANOTHER W-2?

You started off with your first W-2 and your refund looked high?  Then you added another W-2 and it stopped looking so good? That is normal.  When you added more income, your tax liability increased, so you saw your refund decrease.  The program began by giving you your standard deduction—- which lowered your taxable income.  (if you are filing joint it took $25,900 off your income right off the bat)   So you are not being taxed on as much of the income on that first W-2.  Then you added taxable income--so the refund went down. Your refund (or tax due) is based on the total of your income, not “per W-2.”  Wait until you have entered ALL of your income and credit/deduction information.  You can't really tell anything until it is all entered.  That “refund monitor” does not mean anything until everything has been entered.

https://ttlc.intuit.com/questions/2273878-why-did-my-refund-drop-when-i-entered-another-w-2

Yes that is common. It just looks that way because you put them in as separate W2s and saw the tax due change in between them. If it was all on one W2 you would get the same result. And each job was withholding like it was your only job.

Because you only get one standard deduction no matter how many W2s you enter. Turbo Tax starts out by giving you the Standard Deduction. You entered more income when you entered the second W2 but you didn’t enter more deductions. And each job only withheld taxes like it was our only job for the year. You might want to adjust your withholding. Also as you add more income you might not be getting as many credits as before like the EIC credit.