Cheap & convenient resort for young children?

Hello - I know skiing with kids can be expensive - and our enforced ski break lasted 20 years , until we took the bull by the horns and decided we just had to afford it ! our first visit was to Bulgaria - Borovets , which our 3 children loved as this was their first ski trip - we however knew that there was much better if we could afford it. So we bought 2 timeshares - one New Year week , and one a floating Easter week , both in Zell am See in Austria, where we started our Austrian love affair. Our kids enjoyed 2 holidays each season , and I still have one of those timeshares which I use to exchange for other destinations . This is because I now live in Austria, have a business here and would like to help you if you wanted to contact me.
You mention your 3 year old - My grandson was here to visit me in January , he is 3, and joined ski school on Sunday - not too happily I might add - and on Friday he very happily skied 15km , with his ski group, and then proudly asked if I was impressed. I know all kids are different, but don't block out the possibility of ski school altogether as certainly in our village their is excellent instruction for little ones, and also a kindergarden for non skiing tots. This is obviously going to take up a bit of your budget , but it is a real long term investment and worth it if you can afford it.
I am located just 1 hour from Salzburg airport- I too am based in the North of uk, but generally travel from Stanstead as it offers more choice and flights in the week. I say this because in January/Mid March I am open to offering non Saturday arrivals, so this can reduce the flight cost, and is less busy. Sunday is a good option !
Car hire is quite cheap, and the drive is easy and quick. Public transport is also available but when you are 4, it is nearly as good to rent a car.
My apartments are well equipped and offer you all the home comforts, close to the lift, and within walking distance of the supermarket. Rental is arranged through our trusted partner in the village , who gives great care and attention, plus 10% discount to our guests. Children up to 6 get free skis and boots when 1 adults rent.
In Mid March to end of season , kids up to mid teens will get free ski passes when an adult buys a 3 day or more pass , but little ones are free anyway throughout the season.
It is absolutely best if possible to avoid school holidays, as this is much quieter all round for both you an the kids- and of course sadly soon you will be spending the next few years tied to school calendars and airlines who hike up the price like crazy to cash in on families with children . Unlike package tour companies, my prices are not increased at school holidays,we have low,mid and high season prices but generally there is a 5/6 week higher price plus Xmas and New Year.
The snow record in my village is excellent, and we enjoy a unique micro-climte here, with many North facing slopes holding the snow until well into Mid April- so good for late Easter holidays when school restrictions start.
I would be more than happy to offer you further help if you were interested - I understand the need for a holiday with a tight budget, and try and offer the best value possible, without being a cheap package option . Please feel free to ask questions , and I hope I can help you. www.austriaskiapartments.com Nadia Race

I would second Pila. Fab resort with great slopes. If you are looking for a package, Interski will be running their own nursery/ crèche facilities with some ski tuition for the little ones. We have stayed in Pila and Aosta, both are lovely.