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Thank you for your question.
As for the 401k withdrawal to remodel your house, there is no hardship waiver for tax on this distribution. This is because the amounts in a 401k account are generally all pre-tax amounts. The contributions to your 401k were never taxed previously. If you had any after-tax contributions in your 401k account, then a portion related to the after-tax amounts would be non-taxable.
If you were under age 59 1/2 (or 55 with full retirement), you could qualify for an exception to the additional 10% tax penalty but since you have met the age restrictions, there will be no early withdrawal penalty.
The good news is that you will probably qualify to claim the children as dependents and receive child tax credit.
Hope this helps,