I can't fine Tocoo's one-way details for Matsuda. So, I can't make sure the Matsuda from Tocco is free or not. You should better to ask them directly. In Matsuda webpage, it is free within 50km; but it may a special contract between Toccoo and Matsuda. I am very sure that Toyota and Nippon car rental company won't charge one-way fee within the same prefecture. Hachinohe is Aomori, so it is free for the fee if you rent from Toyota or Nippon.
Many Japanese tours are shown such destinations you wrote. Most are based in Sendai; they drive to Towadako after visiting Koiwai Farm, and visit HIraizumi and Matsushima when return. Aizu-Bandai-Goshikinuma in Fukushima Pref. trip is another trip. Japanese tours are mostly 2N3D. Your travel time is long; so you can do it once.
I think you don't need to fly to Aomori. If you like to fly to Aomori, I think you don't need to buy JRs; you can pay one-way fee instead. Or You will fly back from Sendai or Akita: there are fly + drive packages by JAL and ANA.
Also, you can have a car hire twice. Go to JR Koriyama and then have a car rental; visit Bandai/Goshikinuma area, then drive to JR Fukushima. Koriyama is Fukushima Prefecture. Next is go to JR Sendai by train and start to a loop travel.
I had a Aomori trip Tohoku two years ago, and staying in a ryokan called "Yasumiya Keigetsu Tei" in Towadako was memorable. The ryokan held a Nebuta Matsuri show every night. Beside Towadako and Oirase, Shirakami Sanchi and Hirosaki town were nice to visit.
I went to Goshikinuma in Fukushima last fall on 1N2D by car from Tokyo. I needed to pass through Nikko-Kinugawa and then went to Inawashiro-Goshikinuma-Urabandai. So, if you do the same route as me, you don't need to buy a JR pass. As you know, you can go Nikko by a private train from Asakusa. JR Fukushima-JR Sendai won't charge a lot: (JR local 1,280 yen, Highway bus 1,000yen) etc.
You are doing a big Tohoku driving vacation. It looks long drive, but it won't so long as you think when you are doing sightseeing.
Here is driving suggestion routes. Use online translation.
Tohoku is with rich culture, you will see lots of green (scenic)! Have a nice trip!