Let's suppose that at least some of Chad's children believe he really has visions and sees future events. All Chad would have to do is tell his children he "saw" Lori as his future wife in a vision. Or he could say his deceased grandfather came to him in a dream and said it would be "a blessing" if he married Lori. If his children believe in Chad as a prophet, then he can get away with whatever he wants to (with them anyway), as long as he couches it in the wording of "I had a vision..."
I read all through Chad's old blog posts, too, and noticed this pattern. It's likely that some or all of Chad's kids were his first "followers" as far as believers of his visions. One daughter is very close with the famous author, and was the voice for the audio versions of that author's books published with Chad, and vehemently defended that author.
We can only speculate, but these kids also likely aren't the first in their circle to face their widowed dad remarrying really quickly. Quick engagements/first marriages and quick remarriages (especially by widowers) are more common in the Mormon population than in the general population. Almost everyone knows several people who were engaged within two or three weeks, and at least one widow/widower remarried within a month of their spouse's death. "Once you know, you know." The reasoning is usually backed by "we prayed about it" and had a witness of the spirit.
I'm not meaning to veer too far into religious beliefs, but only to say that if Chad said it was "meant to be," it might be very difficult for some or all of the kids to get on board with, but there would be precedent and they would likely fall in line and deal with it. Their dad is young and they surely didn't expect him to be single forever (or even for long). In Mormon theology, everyone grows up knowing men can be sealed to more than one woman (married for eternity). Only one at a time, on earth (currently), but they all end up together in heaven. So, religiously, Chad wasn't throwing Tammy over for Lori, but merely adding Lori to the mix. Plus, if Chad and Lori didn't ever get sealed, this was just a marriage "for time" (until death) and the kids' mom would always be the wife in heaven. The timing is super quick, but I doubt they knew much about Lori other than that she, too, was part of the same crowd/beliefs (both in terms of Mormonism and also the spiritual prepper stuff), and was not married. A perfect match!
Tammy and Chad knew each other for ten weeks before getting engaged, and they were married three months later. Chad said a woman on his mission saw in a vision (while receiving a hands-on blessing from Chad) the person Chad would marry, and described the girl to him. Later, Chad saw Tammy's photo in an old yearbook and "recognized" her from the vision. So, there is a history of visions and Chad's marriage choices, as well as a history of quick engagements (there's a difference between two weeks and two months, but they're both short, and per the vision, Chad knew *before ever meeting Tammy* that he would marry her.