If you're turning 50, you probably want to go all out - but if you wanted to just do guided bits for only part of the tour, try
https://www.facebook.com/arcticshots - they are pretty new, but is a couple of icelandic photographers I was previously following their work & then they have set this up. They run a few tours - northern lights (when appropriate), Snæfellsnes peninsula day tour, Reykjanes peninsula day tour, golden circle day tour, South Coast day tour - they handle the driving. I am going to try a couple out next time i go. I have never really been happy with my photos on previous visits, so i thought i'd try a different approach and see what happens with some guidance on locations and shots.
There is a car hire offer through I heart reykjavik blog (locally run blogger) from Budget which is a good offer (she also does a walking tour of the city which i recommend) - Geysir were the cheapest I found with all insurances (not including Sad cars who rent out cars i wouldnt trust as a single lone female) but I've not done the trip yet so i can't say if i recommned them yet! But for note, I am renting the most basic of basic, for 3 days so i dont know if bigger more sturdy cars are as competitive on price. No car hire insurance covers damage to the underside of the car, as far as im aware.
Nod is right - the biggest obstacle is the weather, which is you're on limited time/schedule can wipe out planned itineraries - weather might mean i do NO tours with arctic shots, but i'm corssing my fingers! Nod is also correct than in good weather, driving is a piece of p***, on regular roads. Some roads are 'interesting' - the road to Dettifoss is like driving over a cattle grid for 20k & if i hadnt been the one driving my friend would have made us turn back - so if you end up there, dont be disheartened - we were in a suzuki vitara, wouldnt have attempted it in Yaris type thing
This will be my 5th visit in August/September - and a great choice for your 50th!