Since I’m assuming you will want to live stream often to check on your kids, I would recommend a wired security camera. The original Canary is a good option as is Arlo Q. Both will allow you to live stream from anywhere. Original Canary does not offer two-way audio for free, Arlo Q does, something to consider if you want to be able to talk to your childcare provider or children using the camera. Both cameras include free cloud storage.
And that is its job, to keep the camera charged. However, I noticed during testing that it does charge the battery too. When I installed the camera, the battery level was at 40%. Soon after connecting the solar panel, that percentage jumped to 50%. The next day it rained, and the percentage climbed from 50 to 52%. Day three was overcast, and yet the battery level crept up to 56%. Day 4 was a beautiful sunny day, and the battery level jumped to 78%. By the end of day 4, I was at 100%.
UPDATE 16FEB2018: After two weeks, I must downgrade my review... it's become obvious that the Ring Floodlight Cam only detects motion during the day. At night, I can walk through the center of my defined motion zone, but the cam won't record until I'm within 10 feet of it. The defined zone is my driveway which is about 40 feet long and we have 3 cars. As long as the ne'er-do-wells only break into the car parked closest to the Ring cam, they will be recorded. A quick Google search for "ring cam won't detect motion at night" will yield many stories of the Ring product line failing to work in darkness. Apparently, the problem has been documented since September 2017 and Ring has failed to fix it. I must say that I'm beyond disappointed. At least I discovered this in enough time to send the cam back to Amazon for a refund.