I feel that another variable that could be a contributing factor to the independent and dependent variables could be the early childhood friends that a child makes especially in the early teens because a kid would develop with these kids and they would have a great influence on their actions and what activities a child participates in. This could affect what troubles a child gets into and such but I do also feel that a solid attachment to a good parenting background would help a child choose good friends to interact with in their early years but this is something that could affect the child's well-being.
I agree with your evaluation tkegs, however I believe you may take it out a step further on your comment about owning toys and pets: In order to own toys or pets, your family would have to have some degree of wealth, since both are expensive. It also follows that a family with greater wealth is more likely to be able to afford having a parent remain at home during the day, allowing for a secure attachment to form between the child and parent. This explains the affect on your varaible of toys and pets. Good job!
Also, it is known that attending a college often leads to better well being, and since toys and pets would indicate wealth, a means to college, it is quite possible that this could correlate as well.