Suggested UA forum threads
http://www.flyertalk.com/forum/unite...o-infants.html (2012 but doubt anything has changed)
http://www.flyertalk.com/forum/unite...ant-twins.html (much older 2004)
http://www.flyertalk.com/forum/unite...77-200-v7.html
plus suggest FT's
Travel with Children forum for lots of helpful experiences
Bottom line, you will likely find most airlines fairly strict on the oxygen mask rule.