All of these experiences and advices are my own assessment. Please make sure you read governmental travel instructions of the country you are from.
Driving around:
Generally, I didn't consider that safety was an issue while driving.
Some factors to consider are:
Safety in Mérida:
First - Mérida is definitely statistically safe (actually in the Americas it's the top fifths safest city (2023) - only 3 cities in Canada and Irvine in the US are safer). That is also how it feels being there. At the end trust your instincts. I would make sure to take precautions against pickpocketing by keeping your valuables secure and out of sight (which you should do anywhere) and as a woman, I advise not to be alone at night (which is maybe a bit more the case in México than elsewhere).
Safety in Valladolid:
No differentiation between Mérida and Valladolid. We felt safe and followed general precautions.
Safety in Cancun and Playa del Carmen:
Playa del Carmen is a popular tourist destination, and while it generally offers a safe environment, it's advisable to take some more precautions. Again statistically about 2 Mio people visit Quintana Roo Beach (Cancun, Tulum, Playa del Carmen being some of the most famous) locations every year - and there is little heavy crime (shootings, rapes) that tourists fall victims too.
However - It is true that since COVID there has been a rise of Cartel Crime (shootings), that have unfortunately involved tourists. Also taxis have been scamming tourists or even forcing tourists to ATMs to withdraw massive sums of money. Police have been stopping tourists driving by car and asked them to handover the money they carry. And on the beaches at night 2 rapes occurred recently. This is why, the US has increased the safety risk assessment of Quintana Roo to Level 2. Again: Statistically all those cases augments to below 1% of the total tourist population.
Vacation is vacation SO: If you don't want to stress about safety then you can follow our super-safe guideline (which is what we did) - and you be most likely ok:
For women
Many women travel alone in the regions we visited. Yet, the society is surely male dominated and women are not particularly safe. Other than in many European countries your less likely supported by the police or governmental agencies if something happens - so I advise: Don't be alone after nightfall, travel with people you trust.