Getting your dog neutered/crate trained properly (never used as a punishment) will go a long way and so will training. There are many reputable teachers that will be able to assist you in making a well-blended home for humans and animals. Best part is training builds lifelong trust. A well trained dog is confident, happy and socially accomplished. *Bad habits may have to be broken, but older dogs can learn just as well as young ones.
I would suggest that you get online and do some research of all the breeds that combine to make Rusty. Getting to know the breeds can often (not always) give you some insight as to why a dog is acting the way it is. I would also talk to someone knowledgeable about animal hierarchy.
Exercise, exercise and more exercise. If he is part Dachshund, then he is probably true to the Hound Group, fearless and full of playful energy. Use your knowledge of his breeding to develop a play routine that will engage not only his body, but his mind as well. *Try running Rusty around until he is starting to lag just a smidge, then under heavy supervision take both dogs out for a short walk. **If Rusty has a longer back, be careful about (really limit) jumping off of things.
It is never too early or late to teach young children or adults how to interact with the four-legged members of the family. Playtime should always be supervised and if things start to escalate terminated. *Remember to never ever let a child use its hands (this is just as true for adults) as a toy. Animals cannot discern the difference between play hand and “I need this one attached to my body.”