Mark Charlot, 32, is charged with intoxication manslaughter.
Authorities say the victims' vehicle, a blue Mazda 626, was stopped at the intersection of Calhoun near Pershing around 9:15 p.m. when Charlot's black Chevrolet Silverado pickup truck slammed into them.
The mother died. Her two children, who are 10 and 16, were taken to the hospital with minor injuries.
Police say Charlot was having trouble staying in a single lane of traffic as he made his way down Calhoun Street.
"Before he even got here, he lost control and was at least on the grassy side of the sidewalk before impact," said HPD Capt. Kevin Deese.
Charlot was out on bond for felony evading arrest.
Law enforcement sources say he was on PCP at the time of the crash and was speeding. Charlot was arrested.
Authorities have not yet released the mother's identity.
Fatal crash in SE Houston
Follow Jeff Ehling on Facebook and Twitter.