Hi nldogbert
Very straightforward to get a car and driver for the 2 days you need in Yangon.
Standard day is 8 hours, which will cost around 60,000 kyats to 80,000 kyats (USD$45-60)
Car quality has improved in the last 3-4 years, but still best to compare whats available is there can still be quite a difference between vehicle quality.
I can recommend a driver who speaks impeccable English and is reliable with a late model vehicle, if needed send me a PM
As a tip - on arrival into Yangon International Airport, there are fixed prices for the taxis at an approved counter as you come through the arrivals area.
If you find a good driver there and are happy with the trip, ask them for their card. If they are not available for day hire they will put you in touch with someone who can assist also.
Best to get a local sim card on arrival for communicating with the driver and making pick ups easier. Local chat apps used here are Line, Viber and Whatsapp - so if you have any of those its easy to stay in touch with your driver also
Good luck