Northern Areas weren't under Chinar Division, the scouts under a DG had responsibility for holding. If 12th Div had been divided into 2, one would have focused primarily on offense and the other could've held the holding sectors. GOC would face lesser trouble in coordination. I think the I Corps example is fair enough to explain my point.
Reinforcement,Supplies, ammo etc are responsibility of QMG Branch. Had 12th Inf Division been supplied consistently in 1971, the momentum of advance shouldn't have broken. This is what i meant by low priority. As for Scouts further North, they even in a weaker position. And keeping them in weaker position has caused India to make roads in Kargil-Leh corridor and make gains in Siachen.
The terrain on Indian side of IOK is suited better logistically for Military deployment than terrain on Pakistan's AJK, opposite 12th Infantry Division. The terrain on Pakistan side becomes worse where mules maybe required fro RVFC unit. If you divide 12th Infantry Division into 2 Divisions, as you have envisioned, you will be deploying another unit of RVFC for the second created Division, where as more mules on same terrain are not required, better mobility is required -> air lift through choppers. Same for other support units, extra unit of Signals, Engineers etc. Artillery units could also be increased if area of operations and objectives are considered different for both Divisions in case of war. Although more firepower is always welcomed, however attention should be towards diverse forms of fire power, such as aircrafts, UCAV's, gunships, MLRS etc.
Coordination between Brigades and battalions from 12th Div HQ is not a hurdle since lines of communication have already been set up. You have to take a look the terrain first. So far no issues for communication of lack or firepower or coordination on LOC have come up, which means the decision to form a multiple-brigade sized force in this terrain is correct. If something is not broken, there is no need to fix it or experiment on it.
All the units under 12 ID operate on the same terrain at majority of the areas, which is mountains. This means the formation, 12th ID, has uniformity to perform any task (defense or offense) set by GOC or X-Corps HQ. The second Division derived from 12th ID, would be performing the same task in the same terrain, unless that second division is not infantry or mountain Division, the purpose does not stand for it to exist. In other Corps HQ's, different infantry Divisions are sent to different areas for Operations or the divisions are meant to operate in different areas on same terrain or different terrain altogether. Mechanised and Armored Divisions are the ones, which are set to operate everywhere, be it plains or forests or desert. So if a new type of Division (say airborne) has to be created from 12th ID, then yes create it. Thats why i gave example of 34th LID since if air borne, it helps 12th ID as well as FCNA by jumping from choppers onto peaks and holding the peaks till relieved by 12th ID and FCNA. 7th Infantry Division is usually sent east for reinforcing AJK.
Even if you create a second division out of 12th ID, it would still operate on the same terrain, on the same lines of comm and most importantly, its objective would be the same. It would hardly happen that 12th ID is asked to attack into IOK and the second division is asked to defend, either they will both be attacking (one as reserve maybe) or both be defending. But even if one is held at reserve, that is already in place through extra brigades of 12th ID. Why create another Div HQ to hold extra Brigades in reserve. If the position of FCNA becomes weak in the north, then a reserve brigade from 12th ID can be sent further north. If 12th ID already had 3 brigades and was on the offensive and the second Division also was engaged with IA with plans of its won, there wont be a reserve Brigade with any of these two Divisions to be sent North for FCNA. If a brigade was sent from either of these two then that respective Division will need to go on defensive or lose momentum during an offensive. With 12 ID's 6-7 Brigades, the operation shouldn't get affected as it would be planned as such from the start.
Another factor in Mountain warfare is strength of battalions. The Regular Infantry battalions are mostly full strength like their Plain/desert deployed counterparts, however some units like Mujahid/Janbaz force are lesser in strength in formation than Regular Infantry Units. You will also have to check if NLI units are full compliment of 780 troops or lesser for a battalion. Due to humongous nature of 12th ID's formations, the regular battalions compliment weaker NG battalions and vice versa.
A better suggestion would have been to increase FCNA's size and also focus on GB scouts to bring them in par with FC standards. There are 3 brigades under FCNA and GB scouts is also a brigade strength. That is just 4 Brigades up in the North. SSD/34th LID is deployed sparsely so can't be sure which formations under it are deployed behind FCNA.
The foremost task at hand is clearing Siachen, which has become a stalemate and costing both sides dearly everyday. The second task is to clear the enemy from disputed posts near Kargil. The third is modernization of Logistics by putting FWO back in action and creating roads that can handle tons of equipment everyday. This also requires transport aviation brigades attached to mountain formations. Fourth is training of scouts and increasing strength of Mujahid/Janbaz Battalions.