I wouldn't say there was any nefarious intent. If he was born in Kenya, his parents/grandparents probably did not know the law at the time and simply figured he was a citizen so flew back with him. Back then air travel was much easier, a woman goes to get on board with an infant and they didn't need reams of paperwork to prove who it was, if it was a citizen, etc. As for the Hawaiian birth certificate, HI issued birth certificates to anyone who had parents living in HI no matter where they were born. It had to do with some fed law (or perhaps state) regarding HI citizenship, "natural born Hawaiians" had benefits naturalized Hawaiians didn't iirc. ETA I do not know what HI put on the bc for place of birth if they were not born in HI.
Ok, let's look at this logically. Obama was born in 1961, Kenya was granted independence from the British in 1963, so the British were still administering all govt functions. If lil Obama was going to fly out of the nation, he's going to need a passport, and given that during the time there were no direct flights to Kenya, there's going to multiple locations where paperwork is needed. Nevermind the fact that it's a white girl carrying a black baby, which is sure to turn a few heads. Ok, so lil Obama reaches US customs, and custom officials seeing a white girl with a black child (IN 1960s AMERICA) just waves them through sans any type of documentation? LOTS of fail would have take place to believe your possible version. The British would've failed to issue a birth certificate, then they would've had to failed to issue a passport. Airline workers in Africa, would've had to been remiss in their jobs. Once in America, customs would've had to drop the ball in a display of epic ineptitude. For a country that kept meticulous records of immigrants during the turn of the last century, the odds would be astronomical, that such could occur repeatedly, with out a single piece of documentation existing.