Both my kids were like this (1 boy, 1 girl). It seems that they just go through a phase where they want to be held almost constantly. The swing worked for us for a while, but I had to almost watch the clock before I could lay them down. Babies have different sleep patterns in the respect that when they fall asleep, they fall into a light sleep. Tell her to try to wait at least 10 minutes before trying to lay him down. At 6 weeks, this only worked about 25% of the time for me. It got exhausting because they did it ALL day, not just once or twice. At least he has this pattern during the day, and not while she's trying to sleep at night!! (been there, done that... wouldn't wish it on my worst enemy!)
Also, nursing on one breast is completely normal. Neither one of my kids ate on both breasts at one feeding. Some has to do with mom's milk supply, some on baby's stomach size, some on baby's appetite. Many people don't view babies as "human beings" with their own appetites, etc. They think that babies eat the same amount at the same time every day, and it's just not true. It's great to hear that mom's milk supply is sufficient enough that he can be satisfied on one breast!!!! Go mama!
As far as everyone questioning her milk supply, please tell her to try not to let outside pressures get to her. The only thing she needs to pay attention to is her baby. Is he growing? Is he alert and hitting his milestones? Does he engage eye contact and smile when awake? This is what matters... not what everyone is telling her. I mention this because even as strong as a mama can be about her decision to breastfeed (or not to), the constant questions, doubts, and sometimes downright belittlement can be exhausting and start to wear at a person, especially a new mom who has a lot going on as it is :)
Congratulations to both you and your sister! Tell her it sounds normal to me, but if she gets concerned, talk to the pediatrician to rule out medical issues (like reflux, etc).