By law, a company must always put the interests of its shareholders first. The insurance company is obliged to keep its payouts to a minimum.
Obviously, the insurance company also has a contractual obligation to you, but that obligation is simply to ensure that you can have the damage repaired. They have offered to get the damage repaired by their own contractors but you've rejected that offer. They will know that their contractors occasionally 'under quote' but their experience (and the knowledge that the contractor doesn't want to lose a major part of their business) will tell them that they'll generally 'get a good deal' from the contractor (and thus satisfy their obligation to their shareholders).
The insurance company will also be aware that the first question many independent companies ask the householder is this one: "Is this an insurance job?". (It's amazing how many companies will suddenly inflate their quote if the answer is "Yes"). Because of this, insurance companies are wary of engaging the services of independent contractors and there's definitely no way that they'd consider effectively 'writing a blank cheque' by allowing them to increase the bill at a later stage. (As I've indicated above, they'll permit their own contractors a certain amount of flexibility because they know that the contractor won't 'try it on', as to do so would result in the contractor potentially losing a major contract).
Your best option would be to ask the insurance company if the offer to use their own contractors still stands. If it does, accept it. If it doesn't, you might be better placed to seek an increased offer from them.
Chris