Ok, so here goes. Judging by the way modern movies are made, it'd be fairly easy to figure out what kind of movie it would be...
The story will follow a young black teen, named Martin, and his poor (but not so poor it's offensive) mom, and younger brother. Mom works full-time at a [Insert employment that is factually accurate while avoiding insensitivity. IE. Call Center] while in her third year of Nursing School. His younger will just sort of be there, but maybe use for a pivotal plot-point in a sequel.
Martin is awkward. He isn't unattractive, but he isn't anything special either. He's got a couple of semi-close friends, and horrible luck with the ladies. He also has aspirations of becoming a rapper, and even has a some ameteur work he's mailed to some bigger Labels, who mostly ignore him. He has, however, found some success on Youtube, where he's slowly gaining traction. He goes by the alias M.C. Fly.
He's friends with a middle-aged divorcee who lives down the block. She's weird, awkward, uncomfortably energetic and oddly attractive. Think of a woman somewhere between Huxley from Demolition Man, and Tannis from Borderlands. Her name is Emily Brown. She has a daughter that will most likely be used as a love-interest in a sequel, but for now she's not been introduced.
He uses her lab equipment, and military-spec computers to help produce his songs and run his Youtube Channel. In return, she helps him with his homework and tries to help with his highschool drama.
It turns out she's the definitive mad-scientist. She spends her days tooling away at various failed inventions with the goal of [whatever todays big topical environmental issue is.] She ran her previous marriage (and family fortune) into the ground with her work, and has since moved into a rundown storage barn.
She will conclude that the only way she will have hope to fix humanity's future, is to fix its' past. So, in completely secrecy, she creates a Time Machine out of, you guessed it... A Prius (or a Tesla, depending on the budget and how Topical they way to be)
The movie will damn close to the original with them meeting up to the mall. The Prius, however, will no longer be "Nuclear Powered". Modern day audiences are scared of Nukes. So it will be some far-fetched bleeding-edge tech she stole from the Military. This also fixes the Libyans (who are far too topical) from finding and (completely off screen, mind you) killing her. So the Military or one off a number off government acronyms will do it instead.
Now, here's the hard part. How far back in American history can you send a teenage black dude, before it gets a little too ... real?
Anything beyond the 70's and he's fucked. So guess were he's going? That's right. 1979.
Now here's where it get's even harder. In order to avoid the appearance of racism, he can't put on Marty's shoes and time-travel to fix his parents. Because the whole "daddy walked out when I was young" thing, is far too real. He won't be able to do anything to benefit his future self, because that will fuck everything up. So we're left with but one option.
Martin will travel back in time to save Emily. Just like the original, albeit, in a slightly more than roundabout kind of way.
He'll pop into being in Dauphin County, Pennsylvania and cause a huge multi-car accident. One of those cars will contain his parents to be, on their first date. This will cause the whole "his disappearing" thing. He'll instantly hide the car, and come back to help, recognize his mom, find a payphone and call for help. His father survives with a few broken bones, and his mom is treated and released.
After ensuring they're survival, he'll go and find Emily by going to her house. There we find her being physically abused, and when she runs out of the house, he intercepts her, only to realize that she's roughly his age. And guess what. He falls for her. So he helps her run.
They make their way out of the neighborhood. At this point, His daughter has come home in a few hours, so Emily's dad calls the police. Queue city wide manhunt. On top of that, The Prius has been discovered by the local PD and reported to the FBI. The car is hauled away to be dismantled and studied.
Emily surmises this, and together they head to a friend of hers to procure a ride, and follow the Prius onto a military base. Martin says he's not going in there, she convinces him by revealing that her dad is an Admiral, and she has nearly free reign of the base. So after some sneaking about, with some comical ducking and covering, some rolling, some slapstick, and some falling and catching they find the Prius and steal it back.
But, as would be the case, the "energy source" has been removed, and lies in pieces on a nearby table, but pretty much everything else is intact. The take the pieces, and flee. This secures the "lightning bolt to power the time circuits" thing from the first. While ensuring that the timeline isn't too fucked.
They run from the authorities. Well... As much running as you can do in a Prius. They hide. The wait. They hope. They get spotted. So they keep running. They choose to split. She'll take the Prius to an old barn her parents never use, and he'll take a cab back to the hospital and check up on his parents.
Turns out that they're both fine, but his dad didn't think she'd want anything to do with him after the accident, so he's been avoiding calling her. Martin tries to convince him otherwise, but he'll stand firm. The next section of the movie will be about him finding his mom and convincing her to go to him. Which she will do, after some initial resistance.
He'll drive her there, his parents will embrace after some awkward banter, his dad will use a catchphrase he heard his mom use often, they'll embrace, they'll kiss. He'll survive.
Now it's time to get home. At this point, I'm not sure if they'll use the "Save the clock tower" bit to hearken back to the original, or come up with some other bullshit. However, in 1979, Three mile island nearly went boom, so I think we could use that as a means to energies the prius. That sends Martin home, and uses an event that already happens to do it.