I would recommend you a slight change in plan:
as proposed in red text.
you can also make it to keran and stay there for the night at first day.
travel time on your own car would be as below:
Lhr to isd (4hrs) and isd to mzd (3hrs) and mzd to keran (3hrs) = total of 9hrs travelling.
You wont have much to do in mzd in you leave lahore early and reach mzd in afternoon.
So for day-1:
Leave lhr by 6am, hav lunch at mzd and proceed for keran. giving break/lunch 3hrs, you should reach keran by 6pm.
Day-2:
have proper rest, leave keran at 9am and you will reach sharda by 12noon (3hrs).
Roam around, visit sharda and enjoy tea and snacks at river side.
Leave sharda by 4pm and you should make it to kel by 5:30pm max (1hr drive, preferably on jeep/bus)
Now this is the tricky part, if you re travelling by car then arrange to leave it at sharda, or at keran to be safe.
Day-3:
this is again gonna be a hectic day:
better to visit arrang kel first as it involves trekking (2~2.5 hrs).
If accompanying kids then it can take more time and stamina.
but then you will have to spend night at taobutt.
Leave kel by 7:30am, trek to arrang kel and reach by 10am. explore and relax.
leave arrang kel by 1:30pm, you will make it to kel by 4pm.
leave immediately for taobutt and you shud reach there (by jeep, ofcourse) around 7:30pm.
You will find very less time for lunch.
Day-4:
if you really have to come back,
Leave taobutt at 7am, you will be kel by 10am.
Sharda by 11am.
Keran by 2pm.
Muzaffarabad by 5pm.
isd by 8pm
and lahore by mid-night.
and i have not given any time for breaks/meals in between as it would be pure travelling time and you will decide for yourself where to take a break.
I might have made some errors for the day-3 but the generous PWers would correct me in that case.
Looking at all that i have explained, i can only recommend you to add another night stay or go through this night-mare.