what do you mean by 'money is tight'?
ime, if you've never been before you need to pay for lessons. Many ski resorts have rules about no-one self teaching or instructing except the people that are licensed there. Unless you're a superb instructor yourself, it really won't work well unless you do pay for lessons.
You can prbably get the price down a little from this, but ime, by the time you've paid for flight, accomodation, lessons, lift passes, meals etc, then you should budget at least 1,000 pounds per person per week.
If you drive there, or find a good all-in deal, you could possibly get that down to 800 per person for a week. Of course, which resort you go to makes a big difference.
If you go to a cheaper resort, usually that means that the snow isn't so great, and they may not have any or enough by Christmas. Feb half term much more dependable.
The 8 and 5 year old are unlikely to ski all day - you will need to pay for childcare or only ski when they ski (then leave your lesson/ski-ing early to be at their pick up on time)