Is there such a book that has all the Proper prayers for daily Divine Liturgy? As I watch the streaming of Daily Divine Liturgy from Canada, I am a little confused how they choose the daily propers for the liturgy when they are not included in The Divine Liturgy An Anthology for Worship (2004) for a particular day. I'm specifically referring to the daily services from St. Josaphat Cathedral in Edmonton, AB, Canada.
There isn't one book. For the Ruthenians, the Metropolitan Cantor Institute has the propers derived from the menaion in a 12 volume series. Generally, the propers are picked from either the day of the week, or the saint of the day, or a DL for the deceased. The prokeimenon and alleluia are from a common set related to the main commemoration. My guess is there is a typikon the cathedral is using to determine what is commemorated, in conjunction with the celebrant saying, "We're doing this or that".
The MCI and the Typicon were/are my recommendations too. See The Common Typikon
and 2021 Typicon
for starters for the Ruthenian usage. The MCI is very thorough and also includes musical notion. Fr. David's Typicon gives all the directives and resources, in full, so more for a monastic observance, but then it can be adapted for parochial or personal prayer. Attached is a sample page, to give a preview of what it contains, from the (probably) 2003 Typicon of Fr. David.