When you add the kids and your current wife to the deed, are you making a gift to them of part of the home. Gifts to your wife don't result in gift tax issues. But gifts to kids do.
As for income tax issues, there are two situations to keep in mind, which I'll explain by examples.
Example 1. Amy and Bart are husband and wife. They have two adult kids, Cindy and David. Let's say that Amy and Bart buy a home for $550,000 in 2010. They don't gift any part of the home to their kids. They live in the home all the time they own it and they sell the home in 2021 for $1 million. They have a gain on the sale of the home of $450,000 (the difference between the sales price and their basis in the home, the $550,000 they paid for it). But because they both owned the home and lived in it for all of the five years immediately preceding the sale they are eligible to exclude from income up to $500,000 of gain from sale of their home. Since their $450,000 of gain is less than the $500,000 maximum exclusion they pay no income tax on the sale of the home.
Now, suppose instead that Amy and Bart add Cindy and David to the deed of the home in 2015, so that now Amy, Bart, Cindy and David each own 25% of the house. At the time they do this, the house is worth $750,000. Amy and Bart have to file federal gift tax returns for the gifts they make to Cindy and David since those gifts to their kids amount to $375,000. They file the returns, reducing their lifetime unified credit against federal estate and gift tax but don't have to pay any actual tax. So far, no tax to pay, so all is good. Again, they sell the home in 2021 for $1 million, with half going to Amy and Bart, and Cindy and David splitting the other half. Amy and Bart now are getting $500,000 from the sale and their basis is $275,000, giving them a gain of $225,000. Again, their gain of $225,000 is less than the $500,000 of gain they can exclude so they pay no income tax on the sale. But Cindy and David don't get that credit because they didn't live in the home. They are adults who have been living in their own homes. Cindy and David together also have gain of $225,000 ($112,500 of gain each). So they end up paying tax at a long term capital gain rate of 20%, for a total income tax paid on the sale for them of $45,000.
In short, by giving Cindy and David half the house there ends up being $45,000 of income tax paid by Cindy and David where there would have been no income tax paid at all if Amy and Bart had not added the kids to the deed.
Example 2.
For this example, we will use the same facts as before, but now Bart dies in 2021. He gives his share of the home to his kids in his will, so that they end up owning half the home with his surviving wife, Amy, still owning the other half. The home is sold shortly after his death, again for $1 million. When Bart dies, the basis in his half share of the house gets reset to the fair market value of it, meaning that his half of the house gets a basis of $500,000, the same as its value. His kids get that basis when they inherit it. So when the house sells, Cindy and David have zero gain and therefore pay no income tax on the sale.
Amy's basis in her half in a non community property state in unchanged, but she'd still pay no tax because she'd still get the benefit of excluding gain up to $250,000 and her gain on her half is $225,000. (If Amy is in a community property state and Amy and Bart hold the property as community property then Amy gets a reset in her basis, too, again resulting in no tax paid by her on the sale.
But instead suppose that Amy and Bart give their kids half the house in 2015, like in the first example, so that they all have 25% ownership. There would be the same gift tax issues in 2015, of course. Then when Bart dies, he gives his remaining 25% share of the house to Amy in his will, so that again the result is that Amy owns half of it after he dies and Cindy and David each still own the 25% of it they had before his death. Because Cindy and David got their shares BEFORE Bart died, this time they don't get a step up in basis. They are again going to pay that $45,000 in income tax on the sale of their shares. (Amy still pays no income tax on the sale of her share, though I won't walk through the exact details of how that works out.)
So, again, the gift of half home by Amy and Bart to their kids before they did results in $45,000 of income tax being paid when the home sells where no tax would have been paid if the gifts before death had not been made.
The exact details of the value of your home now, what basis you have in it, and the details of the later sale of it matter, of course, and depending on those details the results may come out differently and there may not be such a difference in the income tax between making a gift now as opposed to waiting until you die to do it. Also my examples are a bit simplified to illustrate the principles involved. You might want to see a tax pro to crunch the numbers for your situation so that you know how this plays out for you.