Strictly, their first point of call is your TA unit, which should have a Regt Welfare Officer. I'm sure ours does but I've no idea who it is ... (actually, it is probably SO2 CVHQ, but?)
Secondly, there is also the rear party for the unit you are mobbed with (but they could be time zones away from your nearest and dearest.) Chilwell also provide an emergency facility - call them and they'll refer you (they won't actually, can't, do much themselves and they will ask if you've at least tried to contact the RWO). There is a spectacularly dull but, if you can stay awake, highly informative lecture on this on Mob day 1.
Also you have the notification people at RAF Innsworth, if somebody is dead or dying, and the usual chorus of good people - Army Welfare, SSAFA, ABF etc, etc - if there is other support
The welfare role within a TA regt/Battalion is run buy the ROSO, they attend the Unit Welfare Officers course (UWO). Your regular unit should be onside with theatre newsletters and day trips etc depending how far they are from your home, and should also write an intorductary letter to your loved ones!!!
There should be several levels of support available depending on how good your home unit are (which I would imagine/hope is very). My Mrs got several letters from various levels of my CoC last time, but added to that, as stated, RTMC would shoulder a fair burden if needs be. You will get a load of literature from Chillwell (Including a big A4 envelope packed with stuff for the family). On top of this don't forget SAAFA, the ABF and the Legion.
JCCC rely upon. When I was on Herrick I had a family member at home who was critical and sadly passed away within days. It goes without saying where your head goes but that feeling is known to many on Herrick. Admittedly a REMF at BSN I could not believe how they got me home in less than 20 hours. I missed out all controls, had a vehicle waiting at every APOD, flew up front on herc. Had Brize flight diverted to my North of England civvi APOD with a chauffer civi car waiting on the tarmac and missed out controls again. Even SB where craining their necks to find out what was going on. My faith in HM Forces will never be tarnished after that experience. The movers from RAF/Army where truly magnificent in there professionalism and experience. My unit by the way was shite.
I am the Battalion support for any wives, daughters etc left behind . . . . .
As rest already said if UWO ( we have just changed ours, was on Part 1s last week think the ROSO took on the role, but must admit didn't pay much attention as is not my turn to go this time around).