Convince my dad let us get a dog?

Properly trained, contained (fenced in, supervised and/or leashed) dogs do not run off. Your father was irresponsible and should not get another dog until he knows how to care for it properly.

If you're a minor, minors can't own property, dogs are property, so you have no say in the matter only your father can decide whether to get another dog not you. So to answer your question; "Convince my dad let us get a dog?" You don't.

He can just keep the dog on a leash and/or make sure the dog is trained well enough that the dog won't run off. Preventing dogs from running off just requires having a dog on a leash whenever the dog is going outside where there dog could run off. Local laws usually require this anyway.

There are also breeds of dogs which are more likely to run off than others.

It's important to take the dog to obedience classes for the first year or two of its life, so it comes back when called. Always carry biscuits in your pocked, and reward him when he comes back

Promise to always keep the dog on leash...