I'd like to make some extra icepacks to put in my coolbag. The 2 commercial icepacks it comes with don't maintain the temperature for long enough, so I've tried supplementing them with plastic bottles of water that I've frozen. This works reasonably well but are there other containers that would work better and is there anything I could add to the water?
Use a mixture to modify the water's properties
You could use an antifreeze/water mixture that you put in a bottle. You will have a much lower freezing and higher boiling point that just water. This will allow you to keep your frozen packs at a lower temperature than plain ice for longer.
You will also need to be extremely careful with antifreeze around food and/or drinks as it is toxic to almost all mammals. Other creatures may also have toxic reactions to the antifreeze. Insure that if you use a recycled water bottle that it is extremely difficult (aim for impossible) for you and/or children to get into it.
You could also try using alcohol instead of water. It is the same principle as mixing antifreeze with water. It is also much safer than antifreeze, but you will still need to modify the bottle to prevent child access.
Insulate your cooler more effectively.
You didn't mention what type of cooler you are using, so I am guessing that you have a standard injection molded plastic cooler. If you have Styrofoam, then this answer won't work for you.
Drill a hole into the injection molded plastic at one corner so that your hole makes it between the layers of plastic. On the opposite corner, drill another hole so that will allow air to escape. Buy a can of insulating spray foam at your favorite hardware store. Following the instructions on the can, spray the foam into either of the holes you drilled previously. Once you have foam flowing out the other hole, you will want to rotate the cooler to get the foam in as many places internally as possible. Use the quick curing foam so you don't have to tape the holes closed. Let it sit as per the instructions on the can.
If you find that you have missed sections of the cooler, you can always drill more holes and repeat the steps as necessary.
I've never done this myself, but I've camped with people who have used dry ice to keep things cold/frozen over the course of four days.
Dry ice is much colder than regular ice, so you may actually have to insulate things you don't want to freeze from it. Keep it at the bottom of the bag, or maybe move it to the top if it isn't cooling as much.
It's a bad idea to hold dry ice with your hands, so think about plastic bags and tongs.
I would also say that dry ice is a "slower" coolant, so try not to open your cooler as much.
The "R" value of the cooler insulation as well as the seal around the lid are important in retaining the cold. The size of the cooler is also important because the ratio of ice to the product you are trying to keep cool is also a factor. You can get pink RV anti-freeze used to winterize drinking water pipes and tanks in boats and motor homes It is I would assume non-toxic if accidentally ingested. Ice packs made from anti-freeze would probably cool faster to a lower temperature but not for a longer time.