I need to connect together 2 pieces of cardboard as I am adjusting side of the box that will need to sit on top of the fridge (I cut some cardboard off). Would glue be safe? staples? scotch tape? the tiels are supposed to be chewing the box afterwards

If they're going to chew it then I wouldn't use staples or tape. Nontoxic white glue like Elmers would be OK, but don't use a smelly clear glue. Go for something that's safe for young children to use.

I actually decided to sew it together not sure how long it would last in this state but I will try.