You can deduct a portion of the travel if you are self-employed and the travel was necessary for your job. The IRS allows you to deduct expenses that are "ordinary" and "necessary" for your job. If it is ordinary and necessary for you to take the trip for your work, then the travel expenses are deductible.
If you got audited, the IRS might be skeptical of your claim that the trip was for business if you took your family with you, however. So, it is up to you to determine if the trip was for business and to provide documentation to support your decision if you decide to deduct the travel expenses.
If you do deduct the travel, you must segregate personal from business expenses. For instance, you could only deduct the cost of your meals, not those for your family. Expenses for personal things, like trips to amusement parks, would not be deductible if not related to your business work.
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