You can do both trips Neelum Valley and lower Kashmir in this time. But these have to be quality trips with fewer destinations instead of running through the places.
You can contact any of following for advanced booking:
Valley Tracker: Neelum Valley
Awais 0302-8540000
Kutton Hydro Guest House
Hydro Booking No. 05822-921063 and 05822-432245 they don't tend to give booking and u need to collect slip from their office in muzzaffarabad
For Kutton
AJK Tourism: AJK Tourism & Archealogy Department
Friends you can book ajk tourism guest houses from ajk tourism office Muzzafarabad at these numbers 05822-921317 contact person Miss Rabia or 0300-5154292 Mr Raees Khawaja Assistant Director. They can fax you the booking slip that is to show in the rest house.
Neelum Valley:
Day 1: Reach Muzaffarabad in 2-3 hrs and do breakfast there. Visit Pir Chinasi if u want. Then move onwards to stay in Kutton. Get the booking slip from Muzaffarabad. It is a wonderful place to stay.
Day 2: Move onwards to Keran and stay in Valley Trackers here as they have better facilities. On the other hand, there is a village above Keran called Upper Neelum. There are AJK huts up there and views are awesome. If u can compromise a bit on facilities then u can stay and enjoy the view there. Otherwise do visit Upper Neelum for some time.
Day 3: Visit Sharda and explore the town. I hope so some part of spring is still there for u to see as spring is very beautiful in Sharda.
Day 4: Return journey.
Lower Kashmir:
Day 1: Banjosa Lake and stay there
Day 2: Toli Peer visit and stay in Las Danna
Day 3: Reach Muzaffarabad and visit Pir Chinasi. Stay in PC MZF or Sangam Hotel
Day 4: Return through Murree or Nathia Gali