My Dad's family Trust names me as first successor Trustee, should he become incapacitated. Is there a trigger for the Trust to take over?

It works better to have one person be both fin and medPOA. Less hassle that way. To avoid suspicion amongst siblings or other family, simply include annual or semi-annual accounting. Transparency is key.

Medical POA typically goes to the more level headed one.

I hear this type of problem amongst lots of people, parents think they're dividing up the duties equally by giving fin POA to one kid, and health POA to another. It hardly ever works out equally, and there's hardly ever any coordination. Somebody should make an app to solve this problem.

Yes i know that. It has to be done legally however they can. I thought was a no brainer sorry.

Your brother can't just give you his durable POA. If still competent, your dad will needs to sign a new DPOA document and name you as the DPOA and send your brother a notice that he is no longer DPOA.

Don't Handle It !
I am dpoa and trustee and have the power to do whats right for my mother. Tell your brother if he doesnt want the job, to change it over to you. He is responsible for it to be right and should he/you do something wrong you can be held acccountable. So he should ship up or ship out, lol ! Besides if he is a good person why doesnt he want more help for your Dad?I wouldnt help him, make him give it up.

The financial POA is obligated to pay for whatever care you arrange. If he refuses to pay, get him removed by court order.
"Incapacitated" would have to be certified by two separate neurologists or psychiatrists OR in a Guardianship hearing in court.
In either case, you need to see an attorney.