I checked with family members from Canton province. 

Their prime tradition is to give two ley see (red Chinese envelopes) with at least one crisp one dollar bill folded into each. You are supposed to give these to unmarried people, which in practice means mostly kids in your family and friends' children. In a large family that means the kids get a great haul of cash, and the adults are out a lot of money. 

The feedback I got was that ley see is always welcome and you can adapt the amount and the custom to suit your situation. In traditional Chinese society the grandmother provides daycare, although modern life has changed that. But it's a very thoughtful gesture to give the providers money; sort of the equivalent of tipping people who provide you with personal services at Christmas, since their expenses are higher at this time, and it acknowledges your relationship and how much you appreciate their hard work.

How you do it is important and adds to making it gracious. It should be cash and if possible the bill or bills should be new. The traditional red envelopes may be hard to find; they are usually available at Asian markets and a few Asian banks, but there aren't a lot of those in the East Bay (except maybe the 99 Ranch Market in El Cerrito).  I'd suggest as a substitute a small envelope in pink/red/gold of a good quality paper. You could fold one or get it at Paper Source. Hold the envelope with both hands while presenting and say Gung Hay Fat Choy (Happy New Year).  You should give the ley see, it wouldn't be appropriate for your daughter to give it.

A gift to both owner and employee is appropriate and I don't know if the amounts should be the same or different. Avoid any amount with a "four" in it, four is unlucky.  I think 60 or 80 would be good since 6 and 8 are lucky numbers. Give what you feel you can comfortably afford, remembering that you should give the same amount next year if they are still providing child care.