I can’t speak for the northern part of the trip, but I drove Mexico City - Playa del Carmen in March. My route went very close to Veracruz, then around the gulf through Coatzacoalcos, Villahermosa - and then through Ciudad del Carmen to Mérida instead of Chetumal. The roads for most of the trip are very good, at least two lanes in each direction until you reach Villahermosa.
Then it gets a bit rough, just one lane and patches of so-so road. You’ll have to drive slower until after Champotón. The roads then become very well maintained again in the states of Yucatán and Quintana Roo (this is the downside of going through Chetumal, some smaller and poorly maintained stretches if you go south of Villahermosa).
As for safety, at least on the main roads it all feels quite safe. You see plenty of families with fully packed cars doing that route. After Veracruz you just have to make sure you don’t go into Guachicolero areas which can be sketchy, but the road is scenic and safe. There’s even diving under an off-shore oil rig from Veracruz if you overnight there, and some smaller beach towns in Tampico on the way.
I overnighted in Ciudad del Carmen. It is a very ugly oiling town, nothing to see there but plenty of Holiday Inn type hotels to stay in. Safe, cheap and comfortable enough for a night. Leaves just a 9 hour stretch to get to Tulúm the following day.
I can’t speak for the boarder and the area north of Veracruz, but this last part is nothing to fear. Pretty cool trip, actually!
Hope that helps!