When this name first came to my attention, it was because they were advertising low price holidays and using 0871 premium rate numbers for enquiries so that when you phoned the outcome was that after a long call you found that the holiday was no longer available at the advertised price etc etc..
I even reported them to Trading Standards in their area as the web site made no reference to the higher phone charges.
Later reports showed some satisfied customers and it looked like they were cleaning up their act.
Meanwhile, some, supposedly reputable, Travel companies (OK Thomson/First Choice! etc)followed their lead with the 0871 usage.
Unfortunately, as with all travel companies, they are there to sell their product at the price that is best for them, not for you.
As I am a pushover for pushy sales people, I always ask for the info and explain "I am taking it to look at it and then confirm I can get the holiday dates, check hotel reviews etc, and if they can't hold the quoted price for that short period of time, then quite honestly I don't want to deal with them."
The good ones I have dealt with have all worked with me and I have ended up with cracking deals, others I do not touch with a barge pole etc.
Just because the icelolly website shows the lower price does not mean that it was ever available or is even now, so you do revert back to the fact that "you were happy with the holiday and price at the time of booking", so chalk that part up to experience and plan a new stategy for choosing the next holiday, meanwhile concentrate on enjoying this one!
On our last Caribbean holiday, we made friends with a family who used a main TO. They had exactly the same holiday as us but we paid over £200 less per person: we did NOT let on, just agreed that they had got a good deal. They enjoyed their holiday at least as much as we did ours, possibly more because of the upgrades they had bagged etc! I did point them to alternative places to select their next holiday for future guidance as they might get a "wider choice!".
I don't see any reason why you should not ask icelolly for an "official detailed invoice" confirming that they havent charged twice for something due to the large discrepancy in price from that advertised on their website, but do not hold your breath waiting as their definition of detailed probably does not match ours.
If you do want to get into dispute with them, check the forum for Ros's details as she could offer you correct legal advice