Twoandahalfgirls. Sounds like you know a bit about HK, so apologies if any of this is teaching you to suck eggs!
The housing budget you mention is good and you'd have a good range of places to choose from including most expat friendly areas in HK island, Sai Kung/ClearWater Bay, New Territories and also Discovery Bay. You'd probably get a house in Sai Kung and DB and NT. For HK island, a decent sized flat, probably with 4 beds.
I've lived in a few places on HK island and also on DB - all good depending on what you like. Only way will be for you to look yourself and make the trade off for your family - because they do all need some kind of trade off.
For DB your husband, and possibly your kids (depending on schools you choose) would need to commute - it's not too bad - a very pleasant 30 min ferry ride, but it very much depends on where they need to get to after that. So can be a 1 hour commute each way once at office/school. I never minded it - read heaps of novels - but in my experience it can put you off doing stuff on the island at weekends. On DB, currently 2 primary school options, and only 1 secondary school option. And it is a bit sterile (but still very nice as long as you like it!).
But you might prefer island - you probably wouldn't get house, but nice flats and also older buildings but large flats would be in your price range, including places like Pokfulam (15 mins to central), Repulse Bay and Stanley. (Plus mid levels of course, but think you may find that a bit urban based on your comments.)
Schools are extremely difficult to get places right now. Your husband should immediately start discussing this with his employer - this is likely to be your biggest headache, so it's not too early to look into this. And if possible you should come visit and get names down, find out if company have debentures etc. For English System - ESF (primary and secondary on catchment basis but still waiting lists for most schools and years), Kellett (primary from reception and secondary up to Y 8 or 9 I think). Kellett very unlikely to get place in primary unless you have debenture. Secondary may be poss as they have just set it up. Lots of other good schools but waiting lists the norm. If you fancy mandarin education for your kids - Candadian International, Chinese International and International Schools Foundation all have reputation for very good mandarin programmes or bi-lingual programmes. Kellett class sizes in primary are approx 20+ I think, ESF 30 kids a class, and some of other schools have smaller class sizes (HK Academy less than 20). ESF are IB schools using british cirriculum adapted for HK, but think Kellett is using same as UK
One thing to adjust for in HK is the school environment - even the good schools have an inner city feel to them - crowded class rooms, playgrounds on roof, etc. The education is good though - UK, Aus, NZ, US, American teachers.. Just mention this as for me that was harder to adjust to than a smaller flat.
Pre schools - take a look at Woodlands and Sunshine House. Both based on UK pre schools and with daily mandarin (definitely in SH and also WL I think.) Schools all over HK.
The other small consideration for your husband is whether you will get club membership. In the budget that you mention this would be normal and if you do, then you may wish to consider living close to the club, if you won't be working. If you live further away you probably won't use so much (and how much you use it may depend on what facilities you have at home.) If you have a club you could always choose older (which tend to be bigger) flats but don't always have facilities.
Bit long but I'm a fast typer!