Nah, you can do it much cheaper than that by not doing a package with a British operator, then using a resort where there aren't many Brits around (so it won't be British half term there). I only started skiing in my 40s and have never taken a package - although we do live in Central Europe so might be more attuned to the weather here, and can speak German. But ALL ski professionals (especially younger ones) will speak some English.
You main issue now will be finding accommodation for the week you want. We always go self-catering flats to avoid expensive chalets or restaurants. Eastern Europe tends to be good value and few Brits, but you have to balance out the lower cost with the lower altitude. You really need the pistes to be at least 1500m, and 2000 is better, to guarantee snowsure conditions, even in February, - and check how many slopes there use extra snow cannons.
Also different resorts have different definitions of what counts as a child or as a 'young person' for lift passes - but both yours should be children still.
Avoid France - expensive and full of the standardBritish operators. Go for a smaller resort, which won't have the super black runs, but you don't need them anyway.
Generally you'd have each of you booked on a 5-6 day course lasting 2-3 hours each day, then have lunch, then two hours to practice what you learned in the afternoon.
You can often get 10-15% discount on gear rental by booking online in advance. Do Splash out on aheated shoe and ski locker at the base station though - so worth it.
An example of a resort we went to in 2017 which was pretty cheap and not overcrowded, and ideal for beginners, was Lofer in Austria - much smaller than the more well known resorts so easier to get accom. , cheaper lift passes, 45 mins from Salzburg airport, cutesy village. The one downside was that it wasn't quite high enough and on our last day the snow went slushy. As a beginner you need good snow conditions to stay upright!