Let me say first off, that sucks, feel your pain, been there done that...
I know if feels like a disaster (and it is) but it's not THAT BAD of a disaster. Also, I'm not a professional builder, although I have done a lot of construction, so take my advice with a grain of salt.
From what I can tell by the pictures, you have two paths (considering the 10k deductible). Option 1 (if you're handy, don't mind getting dirty and have the time) is to just take care of the problem yourself. I'm basing this on the pictures you posted so there may be something I'm missing...but from what I can tell, you need to repair a section of roof and redo a section of drywall. There is also insulation to take care of and the mold/rot concern. I would do the following:
1) Inspect the roof decking for swelling or other damage. OSB does not like to get wet and will swell. If it's OK, then great, if not...I'd re-deck the damaged areas. I'd do this immediately. Next, I'd reinstall new roofing felt (or Tyvek..whatever floats your boat) and get the section over the kitchen dried in as quickly as possible to avoid further damage.
2) I'd rip out all of the damaged insulation from the attic and drywall from the kitchen. You will want to rent a dumpster (they are not expensive). Section off the damaged area of your house with plastic and duct tape to help keep the dust down.
3) I'd get some fans going in the attic to keep the air moving and get everything nice and dry. You can pre-emp any mold issues by spraying the decking and trusses with RMR-86. I'd let the fans run a couple of days-a week..however long it takes to dry everything out. During that time I'd track down exactly what brand/type/style of roof shingles you have and buy however many squares will be needed for the damaged sections. I'd also check out any wiring that may have gotten wet. Pay an electrician for two hours of his time to have a look see if you don't have an electrician buddy that will do it for beer.
4) Inspect any roof penetrations (vents, chimneys, etc) for any damage.
5) Once everything is nice and dry I'd re-roof the damaged sections. Roofing is pretty straight forward and it's a simply process to learn (YouTube has a million how-to videos). Now your house is weather-tight again.
6) Assuming all is good with mechanicals in the attic (and it's nice and dry) you can move onto sheet rock. Again, it's a simply process to hang sheet rock, although you probably will want a buddy. Panels are heavy and a PITA to handle.
7) Hanging sheet rock is straight forward...taping and finishing may be something you'll want to hire out....just depends. Good tape and finish=nice looking wall. Shitty tape and finish=you'll hate it forever and so will your wife.
8) Re insulate....rent a machine from Home Depot and use the blown in stuff of your choice...rockwool/fiberglass/whatever. Depth determines R-Value so you'd need to check with your codes for what's needed (R-38? R-50?). Paint...clean up...beer thirty.
Option 1 see's you spending $5,000 (plus or minus...you may need to rent tools,pay for permits, etc...again based on what I can see by the pictures) and you do all the work and coordinate any needed inspections. I don't know if you need new cabinets or flooring...obviously that changes things. It's also two weeks of your life, a lot of bad words and some donations of skin and blood.
Option 2....Pay the 10k deductible and let the contractors handle all of it. You will be out more money, but you only have to deal with the annoyance of various contractors banging away. You also have to deal with the insurance company and any rate changes that get tacked on next year when you renew thanks to this claim.
If you do go the contractor route...remember the line.."I pay when the job is COMPLETE and has PASSED INSPECTION." Use only high quality contractors that you've vetted through Angie's list/BBB/etc. DO NOT HIRE YOUR BROTHER IN LAW! Do nor fall for the "I need a deposit so I can buy materials" line. If they give you that, your response is "I pay when the job is complete and has passed inspection....I will be glad to purchase the materials for you and store them here on site."
Obviously, there is more to consider and I don't have all of the information. But from what I can see your disaster rates a 2 on a scale from "My House Is Perfect" to "My House Just Got Sucked Into The Ocean Along With My Dog."
Personally, I'd just fix it. Skill-wise you're taking about being able to pound nails, measure, lift stuff, carry stuff, etc.
I know it sucks to have to deal with shit like this. Good luck!