Well, there's a DATA DVD and there's an AUTHORED DVD, as in "created in Encore and plays in a DVD player".
Data DVD's don't play in a DVD player -- they're just a permanent storage medium.
I'll guess the client wants the file burned to a data DVD, but you'd better check.
Apologies, I did not specify. They want a VIDEO-DVD, that can be played in a DVD player.
If the client REALLY wants a DVD -- standard definition, not HD -- you still can use Encore.
But if the client wants an HD Blu-Ray, you'd want to use something like Toast, which can make authored Blu-Rays.
Considering they don't even MAKE DVD players any more, just Blu-Ray players that can also play DVDs, I'll guess you'll be making a Blu-Ray. But again, it's wise to ask for clarification.
Just use Encore. You can do DVD or Blu-ray; it sounds like the client wants a DVD. You can set Encore to use AME for the transcoding, but it is better to export your files from Premiere/AME before importing to Encore.
Use the MPEG2-DVD format, and the appropriate preset (widescreen, framerate, etc.). If it is not a short program, you'll need to sort out the bitrate. If you are downrezzing from HD, in the export dialog, left side, set the crop to "Scale to Fill."
This will create an m2v and wav. If you are using a menu, add it first. Import to Encore "as timeline," selecting both files.
The Encore forum is here: