As my Aunt's POA, I am hiring 2 people to serve as caregivers. I have found a bookkeeper to handle taxes and E.D.D. deposits but still have questions.

What is EDD, employment development department?

I think you should see a Trust and estate attorney; this comes out of your Aunt's account on which you sign all checks with HER name followed by yours as POA. I served as both Trustee of Trust and POA for my brother. That is to say I handled ALL finances, all financial payments and kept the meticulous records that go along with all of that. I put money into an account of his that was his own spending account for incidentals, and would have put more money in as needed had he lived so long as to need more.
Having two people handling your aunt's money would have been too confusing for me. If you see an attorney (and as said her estate pays for this) you can work out how this is best done.
What will happen when Aunt, as Trustee of her Trust, is unable to put money into this account?
I have concerns re all of this, so do see an attorney to work out what your duties are and what you are accountable for here.

That's CPA territory there. Maybe consult one or look for a website Q&A staffed by CPAs to ask the question.

Don't pay someone to get an EIN, though. You can do it yourself through the IRS website.