How much, beyond federal minimum withholding i.e. 20% should I withhold while withdrawing 100%available funds from my 401k account. I am 35 with 3 soon to be 4 dependents

It depends on your other income and filing status.  You will owe a 10% penalty no matter what (but there are some exceptions).  The federal income tax could be between 0% and 24% depending on your other income, deductions, and dependents.  It might be best to try this tax estimator. 

TaxCaster tax calculator

The fact that you will have up to 4 children who qualify for the child tax credit could make a significant reduction in tax, as long as you also have income from working during the year (before and after the break). 

Here are three other points to consider.

1. You can withdraw up to $1000 for any family financial emergency, and not pay the 10% penalty.  (You will still pay the penalty on the rest of the withdrawal.)  You don't need to tell the plan this, it will be taken care of on your tax return.

2. You can also avoid the penalty on up to $5000 withdrawn for the birth of a child, but there is a catch:  

the withdrawal must happen after the baby is born, it does not count for the exclusion if you make the withdrawal before the baby is born.

3. If you are unemployed for at least 12 weeks, and received unemployment insurance benefits, and you paid for COBRA health care coverage, then any amount you withdraw to pay the COBRA insurance premiums is also exempt from the 10% penalty.  This is also something you will claim on your tax return, you do not have to tell the plan when you make the withdrawal. 

I am reminded to add, that whatever tax you estimate you will owe, should be withheld from the withdrawal instead of planning to pay later.

For example, if you estimate that you will be in the 12% tax bracket, plus the 10% penalty, you should have at least 22% withheld from the withdrawal.  If you estimate you will be in the 22% bracket, you should have 32% withheld. If you withhold too much, you will get the difference back as your tax refund.  If you don't withhold enough, not only will you owe a tax payment when you file your return, you could be charged an underpayment penalty for not having enough withholding at the time.  (Taxes are pay as you go.  If you don't have enough withheld and only pay when you file your return, you can be assessed an under-payment penalty for not paying enough into the system during the year.)

And don't forget to have state income tax withheld as well.  States don't charge an additional penalty for early withdrawal, but regular state income tax can be between 3-10% depending on which state and how much total income.