Hi,
I'm living in Singapore and on about the same amount. I will however be relocating to London and have been looking at the same things. Let me share my 11 year experience as an °µÍø½ûÇø here.
Your salary is quite good even for an °µÍø½ûÇø. it's almost unheard of for a local.
$7000 for a 4 bedroom house is a good number. I have a 3bdrm for about 6K in a very nice area. It's 3 stories, almost 4K sqf with a big yard. On average, a house is between 4-10K depending on areas and type of house you want. Unless you want to live in the city centre, you would want to look at places like East Coast district 14-16. East coast is the new in area but prices in housing are slowly coming down. Bukit Timah is also a nice however more expensive area. Look at district 10 & 11. They are pretty convenient areas to get in to town with lots of trains and buses. Taxis are abundant as well.
Schooling here is very expensive. Budget $30-35K per child just for tuition. That won't include books, transport or uniforms plus other incidentals (school trips etc).
At your salary bracket, you can look at probably around 12-14% tax rate. Other things that are expensive here include:
Car - unbelievably, stupidly expensive to buy one. My recommendation is to lease. You can get a very nice car including insurance, maintenance etc for about 2k per month. A down payment on a Toyota Corolla would cost you about 50-60K alone.
Alcohol - Average price for pint in most bars and restaurants around Singapore is around 12-15. Could go as high as $20 in the higher end places.
Grocery - Food shopping at the typical "°µÍø½ûÇø" focused places is pretty expensive. Try to be more like a local and you will get good quality stuff or much less. Think Giant Hypermart or Fairprice Finest and also leverage the wet markets. We try to do a weekly trip. They are in most local neighborhoods so easy to find.
Dining out - Depending on your taste, a family of 4 dining out will set you back $100 minimum. A really nice meal out can be upwards of $3-400.
In summary, Singapore is not the cheap place it once was. For the last few years it has ranked as the most expensive city in the world and the government is actually proud of that. They intentionally want to raise the cost of living to be on par with Tokyo or Hong Kong. You can live as large as you want here.
Leave aside the costs, Singapore is a great place to raise kids. A lot of greenery and quite international with a large °µÍø½ûÇø community. Travel around the region to places like Indonesia, Thailand, Malaysia etc is very cheap and easy to do, which is a great experience for the kids as well. It is also very safe. I forgot my iPhone 7 in the men's room in a large shopping mall a few weeks ago and went back within 5 minutes to find it gone. I called from my wife's phone and someone had already taken it to a nearby restaurant to hold for the owner.
All in all, it was a good experience for us to be here but we are moving on now. I would say it would be good for you as well. Singapore is Asia light so not hard to adjust.
Hope this info helps.