I always see shower signs when I come back through MUC, but have never used them.. I'm guessing it is these..
https://www.munich-airport.com/shower-787635
Similarly, left luggage, if you can't check your bags:
https://www.munich-airport.com/left-luggage-851650
My suggestion would be to grab a shower, leave the bags, and take the S-Bahn into the city. Very well signed, easy to do (instructions in English on the machines), S-8 or S-1 would both work, though S-8 slightly shorter and runs every 20 minutes. 24 or 25 Euro give or take will get you a day ticket for both of you (group day ticket). Head to Marienplatz (45 minute mostly scenic ride on the train), get some lunch, walk around, grab a beer in the bier garten in the Viktualmarket.. all very compact area. If you feel a little more energetic, jump off the S-Bahn at Isartor, and take the tram up to the bottom end of the English garden (5 minute ride), watch the surfers, grab a coffee in Frau whatshernames little cafe and relax there.
8 hours sitting in MUC would be a crime given how easy it is to get to the city.
If you're flush, Uber and cabs are also available, but I find expensive at around 70 euros plus, depending on traffic.
As mentioned upthread T1 is yuck, and the AF lounge there is somewhat prisonlike, albeit it with decent wine :-)
Can also confirm no access to the LH lounges on arrival. I tried and failed.
Failing all of that, between T2 and T1 is an open air plaza which has a model old plane serving beer and curry wurst, so if its a nice day its ok to sit out at. Currently construction work will be going on around you, but not sure when you are going through. Also, T2 has nice restaurants and bars and is generally one of the more pleasant airports to pass through IMO.
Oh, there are also "napcabs" scattered around T2 - not sure of the price, but that could be an option if you need a nap...