This may be going against the grain, but I think the real question the OP needs to ask is whether he really cares whether what he's doing is ethical or not.

Evaluating decisions like this really comes down to understanding your values and owning them.

Values are the measuring sticks by which people quantify success in life. Whether or not we realize it, we constantly measure our actions against our values, and how we 'measure up' determines our self-worth.

In this specific example, there are two conflicting values: integrity and family. They are in direct conflict, which is putting the OP in a stressful situation -- acting in the most honest way here will lead to a worse life for the OP's family. Creating the best life for his family requires that he must lie.

So, the OP needs to ask himself: Do I value integrity? Do I value my family? If I value both, which do I value more?

Personally, I don't think there's really a right or wrong answer to these questions. There's no intrinsic value in the universe -- but assigning value is part of the human condition and we feel fulfilled when we lead a life of purpose (however arbitrary). When faced with difficult decisions like this, it's important to be aware of what your values are. The 'right' decision for you will be apparent.