Depends on whether it would add or relieve stress. The cycling alone should be a stress reducer. It seems you should be able to get home and on the way to childcare within 35 minutes. E.g., allow 5 minutes to "leave work", another 5 minutes to "get home and get on the road", that still leaves 25 minutes to go 2.7 miles: 6.5 MPH would do it, and if you are at all in shape with any decent bike that is easily doable for 2.7 miles.
If there is something that makes the above scenario too optimistic (e.g., you often "can't" leave exactly at 5PM, or there is an often-open drawbridge on your route home, etc.), and the net effect would be added stress - that's the last thing you want just before you pick up your kids.
The choice is yours....good luck!