My mother in law inherited her mother's house (that is paid off). Does she have to live in it for 1-2 yrs because of capital gaines, or can she sell it with out a penalty?

You are mixing several concepts:

1. When a person dies, the basis of all of their property is "stepped up" to the value of death for federal income tax purposes (and most states follow the federal income tax rules). Thus if your mother-in-law's mother purchased the home 50 years ago for $12,000 and it was valued at $550,000 at the date of her death, the heirs can sell the property for $550,000 and will have no gain for tax purposes. The $550,000 becomes what is known as the heirs' "basis."

2. Long term capital gains treatment does not require living in the house, it simply requires that you hold the property the required holding period. If you inherit property, you are considered to have held the property longer than 1 year, regardless of how long you actually held it. If in my example, your mother-in-law sells the house for $600,000 six weeks after she inherited it, she will have $50,000 in long term capital gain (the difference between the sales price and the basis).

3. When you sell your primary residence, you can make up to $250,000 in profit if you're a single owner, twice that if you're married, and not owe any capital gains taxes at all. However, that exemption does require that you live in the house as your principal residence for 2 of the 5 years preceding the sale. If your mother-in-law moved in today and in two years sold the house for $650,000, there would be no capital gain. The $100,000 difference between her basis ($550,000) and the sales price ($650,000) is covered by the exemption of up to $250,000.