If children inherit a deceased parent's home and sell it, do they have to pay capital gains taxes or can they take a one time sale credit?

I am so sorry for your loss.  I would strongly suggest that you seek help with the filing of the estate tax return from an accountant familiar with estate tax laws. What the tax will be and how it is determined will depend on if the estate sells the property (and it is valued for estate tax purposes) or if it is transferred to the children first and then sold.  Remember, that the property is valued as of the date of death of your Mother, not the date of the purchase by your Mother.  This is a significant difference given the rising cost of property.  What this also means is that if it is transferred and then sold there will most likely be no capital gains tax.  Seek legal help.  The tax laws for estates are changing on a yearly basis.  Good luck.