Staying over night on US transit visa

My sister-in-law will be flying through the US on a transit visa as she returns from Europe. She has done this before but this time we had applied for a tourist visa. She was just denied the tourist visa. She currently just has the first leg of the return trip from Europe to Newark. She gets in Newark around noon. Would it be permissible to book her remaining travel (leaving the US from Newark), the next day so she can stay with us (not very far from the airport) for one night? In previous trips where she just had layovers for a few hours in the U.S., they had stamped and dated her passport for several days (almost a month) but the US State department travel website states "A foreign citizen whose layover in the United States is for a primary purpose other than to transit, for example to visit friends or sightsee, requires a visitor (B) visa."

Also, would it be a problem that the second leg of the trip is on a separate ticket? (I realize she will need to show that she has return passage when starting the trip.)