From my personal experience, packing in a day trip bag is only a good idea in theory. It will prove to be unnecessary in the field. The extra lbs and time/effort it takes to swap bags, then keep up with the other bag, then re-pack your other bag will prove to be an annoyance. All quality backpacks these days compress down into daypacks readily, and managing some extra pack will be far less cumbersome than managing another pack.
My advice, buy the largest bag you think you may need. For 4-7 days, the LT 5500 or Pro 6000 should be plenty of room depending on your gear (Meaning weight conscious gear, realistic clothing, average food, average optics). Strapping some gear to the outside is always an option as well. There are plenty of ways to make a 5-6000 CU pack work for a week.
Now if you are hauling a lot of optics, extra clothes, food for two, or are dead set on carrying meat inside the bag, then go for the 7000 or 7800. Again, extra pack will not hurt in the long run as long as you have the discipline to still only carry what you need.
If you are really set on having a day pack, the stalker from kuiu is a good option. It clips inside the packs and weighs a lot less than another pack bag.