Not sure it's realistic to do this as an out-and-back day trip from the city. Check your logistical expectations carefully.
We spent 4 days for this. Day 1, rent car and drive to Angangueo. Days 2 and 3 were spent at the two nearby reserves (one day each). Day 4 was the drive back to the city and car return. That seemed about right for us (and we often travel at a bleeding pace that would make many folks here question our sanity - just sayin', it's absolutely worth it, but be careful about your expectations for the time required).
We rented a car in Mexico City (driving in the city itself is not for the faint of heart, bing your A game - but once outside the DF is easy enough). We drove out to Angangueo in nearby Michoacán, spent three nights there, and used it as our base to visit the reserves (we did Sierra Chincua and El Rosario, both were incredible and well worth the time and effort invested). No tour or guide, on our own (not my first Mexican rodeo).
It'll be very helpful if you can manage some basic Spanish.
Of course, it's serious business, so do be smart in all your choices and behaviors. But take all the dire warnings you will undoubtedly soon be receiving (that you're gonna be kidnapped, tortured, ripped-off by cops and drug gangs, and will surely die a horrible, grisly death) with a grain of salt. Well-meaning and sincere those warnings will be, but probably not from anyone who has had any actual experience in the region. Lots of "a friend told me" and "I saw it on the internets." YMMV.
We had a magical, wonderful experience. So awesome. 🦋❤️😎
Be prepared for it to be surprisingly cold up in the mountains at that time of year (we were there in mid-February). Our hotel had no heat other than a fireplace (the fire was atmospheric, but we couldn't keep a fire going all night and man, it got COLD!). I was afraid that the water in out toilet would freeze overnight, It didn't, but we did. My wife still compares any cold night we experience to the night we slept in that room. Brrrr.