@nancy
Assuming your school gives you a foreign expert's certificate - they should also help you place your kids in a local pre-school (should). Pre-schools in Kunming are heavily impacted, so it'll take a bit of arm bending and maybe a cash "gift" if all else fails. Also - the schools here are utterly retarded compared to major Tier 1 cities. You'll be lucky if they teach your kid how to read and write their own name - the schools are more like glorified unskilled day care centers (my personal experience).
1. Your child/children MUST be potty trained. NO DIAPERS.
2. Ask (thru your translator) if the school teaches the kids normal things such as brushing teach, washing face and hands.
3. Besides finger-painting day and clay modeling day - see if they teach anything such as read/write chinese characters, pinyin, memorizing poems and songs (usually Tang dynasty era). This is the standard for Beijing pre-schools. It'll give your kid a boost if you stay to put them into primary school.
4. You'll need basic health insurance for each child - it runs around CNY 50 a year (or was that per semester - can't remember). A trip to any major insurance carrier should be sufficient - your school MAY provide insurance (rarely) for your dependents - but usually you'll have to pay yourself.
5. Some schools offer boarding - this is convenient if you're late, or want an evening alone etc.
6. TRY to get your children into the Kunming city pre-schools - they're somewhat accredited and MAY offer a pathway to regular Kunming city primary schools (Grades 1-6).
Health insurance check - it varies from province to province depending on the weather - check with your school - but usually children (toddlers and infants) are exempt - they're checking for communicable diseases.
WARNING
Just in case - AVOID immunizations if possible until your kids are 2 years old. This may be problematic if you send your children to pre-school as they REQUIRE an immunization history and up-to-date shots - it's kind of a scam - regardless of country. If you must - make sure the nurse properly shakes or doesn't shake the meds, depending on which med. ALthough unproven (thanks to some serious lobbying by big pharma - SOME immunization shots for toddlers and infants contain heavy metals (aka mercury etc) and some meds are for adults, but they lazily and negligently use them on infants and toddlers OR don't mix the meds properly so your child may receive a serious overdose of heavy metals - causing downe's syndrome type symptoms which take years (and lots of cash) to recover from. It MAY be an urban legend - but why risk it.
GREEN LAKE
I'd probably recommend the beichen (NE) area of KM instead - more expats and expat friendly stores (metro, wicker basket, etc) not to mention what I think is an evangelistic church (never been) if you're into that kind of thing. Green Lake is nice - but severely overcrowded during morning and evening rush hour - which means atrocious air quality and traffic - which means no taxis.
TAXIS
Beware kunming taxis - generally they're pretty good - but roughly 20% (or more) are petty thieves - they'll try to take you the long scenic route to make a few extra ¥ - some drivers can actually double the fare if you're not paying attention. ALWAYS get a receipt. If you KNOW you've been cheated - call the complaint line - the driver will have to come back and refund the fare - usually in full. Also handy if you lose your wallet, phone, umbrella, children, etc.
You are welcome to contact me via PM (Private Mail - see the link at the top of this page after you logon to the site - click your name and then stumble around till you find the PM link).
JOBS
Schools are hiring almost all the time - some english teachers can be rather unreliable - so you'd be a pearl (kids usually means stable aside from the sometimes frequent family emergencies).
Good luck - hope your personal and family experience is idyllic.