There's no place for guilt - ANYONE normal person would feel relief.
Caregiving is a huge physical and emotional burden, no matter how willingly
undertaken.

And sadness and grief is appropriate when anyone dies.  
But Alzheimers is like death in slow motion, we lose a bit more of our loved one
every day, and it goes on for years.  
I believe that we've all done a lot of our grieving long before the actual
death, so don't be surprised if you do not feel as bad as you (or others) think
you should.

And with Alzheimers, death marks the final end of an inevitable sequence of
painful events, so relief that you and your loved one have finally reached the
end of that long and difficult road is also totally normal.

As to the constant little reminders of the one who's gone, I can only say that
these get easier to handle with time.  
As a caregiver, your whole life revolves around your Dad; there'll be a huge
upset in all your routines when he passes.  But you'll build another daily life,
with other interests gradually taking over that big empty space where you Dad
used to be.  
When my wife died, she'd been the center of my life for 25 years, everything I'd
hoped for and planned included her.  
Tomorrow, she'll have been gone for 7 years.  
Now, I've resumed my photography and political interests and can happily think
of her every day, remembering all the fun times we had.

All it takes is time. . .