Maternity hospital behind the GreenLake Hotel is where most people go for maternity care, before, delivery, and post delivery. There's also an excellent Children's Hospital (two branches) in the city and on the edge of town (newer facility). These hospitals see roughly 3k outpatients per day - so be prepared for at least a half day of lines. Best to have "guanxi" for these places if possible - facilitates line-jumping. Kunming and China in general has virtually NO evidence based medical care - so chronic problems frequently go un-recognized.
Formula (if you go the formula way) is rather expensive if you buy foreign brands - we bought New Zealand branded formula for anywhere from CNY 300-600 per can. We bought from local dealers that have been in business for a LONG time - most stores give you crappy gifts like strollers, blankets, etc as you accrue purchase "points".
STROLLERS AND BABY CARRIERS
Get a GOOD baby and infant carrier. You'll need it. Beware thieves on buses, trains, etc - they'll target you as you're distracted with baby things - be aware. Strollers are difficult to use as the sidewalks can be ... bumpy and crowded - and you frequently have to contend with e-bikes zipping along the sidewalks.
At 4yo - you can put your kid into daycare/nursery school - but they MUST be potty trained (no diapers).
Unless you can use your work's guanxi - most nursery schools are more like daycare centers in KM. You'll be lucky if your child can scribble their own name when it's time to go to primary school (assuming you're here that long). Beijing and other Tier 1 cities - kids learn basic poetry and usually have a 100-200 word reading and writing vocabulary - so you'll have to home school to keep them on par with Tier 1 city kids.
DIAPERS & DIAPER WIPES
Diapers - Walmart or Carrefour - we used Pampers - the expensive white plastic wrapped ones for nite times (comfortable) and the cheaper green plastic wrapped ones for daily wear & tear. Wet wipes (non-alcohol) - everywhere - we tend to use Japanese brands as Pampers wet ones are alcohol based - which accelerates rashes and stings. We alternated between Vaseline petroleum gel and French (expensive) branded liniments for rashes - but if your quick to change the diapers - you can generally avoid rashes.
Kunming is at 2km altitude. It gets dry, so keep the baby hydrated - although formula usually does the trick. There's free bottled (water dispenser) hot water everywhere (especially banks!) - for emergencies. And keep your eyes out for fast food restaurants and Chinese 5 star hotels (for bathrooms). Newer shopping centers also have handicapped restrooms - although they can be grubby - the one near our house uses the handicapped restroom to store their dirty mops n stuff.
Sometimes when people move here with newborns - they'll go through some periods of vomiting as they acclimate to the pollens and other dirty things (some adults also). Again - the key is to keep yourselves and the children hydrated. Drink stores (sugar water) and bottled water abound - in an emergency.
Wet markets (farmers' markets) are great for buying most fresh produce - wash fruits etc diligently (another use for bottled water, in a clinch).
Best wishes - the gokm online community is quite warm and helpful, so don't hesitate to ask online. As @Ocean mentioned - use the search feature to mine the wealth of blogged material.
FINALLY - learn to use taobao.com (and translate.google...choose your favorite country) for online shopping. Baby things are ludicrously expensive and it's hit or miss with stores - some sell crappy junk - others...more expensive stuff. The large department stores carry nicer stuff - but significantly pricier.
A blender (either handheld or countertop) is a necessity for blending fruit, veges, and other forms of frappeed (?) baby foods - when your infant gets to pseudo-solid food age.
Needless to say - internet will be your lifeline to the community...but that's another thread. FYI - Facebook, youtube, twitter - non-functional unless you use a VPN - but - that's another thread.
Regards and best wishes - laotou.