I would say not a hope in hell either in Europe or half term and certainly not both.
You do know that a lift pass say for 3 valleys for a week is 300 euros each? So thats 600 euros without flights, food, accomadation, etc. Never mind ski hire, lessons and child care.
You would struggle if you double your budget to be honest.
I go skiing every year in Jan and go as cheap as possible. For 3 of us I can generally get flights, transfers and fully catered chalet (not lunch) for just under 1k - this is a cheap week in Jan though.
On top of that we have to hire skis for dd, 65 euros. Me and dh have our own but if you don't you're looking at 200 euros for 2 x adults.
You're looking at 200 euros per adult for 5x morning lessons.
So thats approx 1400 euros without food, accomodation or childcare. So that leaves you with 1000euros.
Possibly if you drove, went in a self catering studio appt and took all your food with you. But then there's ferry crossing, fuel, tolls.
Food in Europe is expensive. We struggle to get lunch for less than 15 euros a head and that is in a cheap self service place having the cheapest thing on the menu, ie; sausage and chips.