The biggest issue I can think of offhand is that, even with a restraining harness, an 8-week old puppy is not going to want to stay put. A seatbelt harness will keep her from flying around the cabin if there is an accident or sudden stop but not likely to keep her from climbing all over the kids in the child seats.
Since they are front-facing child seats, I'm assuming the children are not infants, so this may or may not be an issue for you (or them.)
Since they are front-facing child seats, I'm assuming the children are not infants, so this may or may not be an issue for you (or them.)