Ah, poor second babies! The bottom line is that you can't give naps as much time and attention as you did for the first one, but that doesn't mean it's all doom and gloom! For sleep training I would say don't worry about it at first. I know that goes against 'start as you mean to go on' but honestly it'll make everyone's lives easier if you can get out and do things together, not spend hours flitting between a bored toddler and a dark room shushing a baby. So pram/car/sling naps when you need to start with, and just the basics of EAS with separating eating and sleeping.
At 3 months or whatever age you feel it is time to get serious about independent sleep - is your older child home all the time or is there any preschool/nursery etc in the mix? Are you alone or can your recruit DH, grandparents or any other helping hands so that you can focus on the baby? You mentioned that your toddler still naps, so that would maybe be a good place to start. Try to get a nap in the crib for the baby at this time when you don't have a LO running around.
Although independent sleep in baby's own bed is obviously the end goal, I would maintain some APOP too as it is actually very restrictive to have a baby who won't nap out and about and have to be home so much. My DD2 is one who only naps well at home (not by my doing, she is just too nosey to sleep if there's anything vaguely interesting going on!), and it is a PITA! I am constantly having to choose between Dd1 missing out on something if we have to rush home, or DD2 being put down late / short napping / not napping and ending up OT.
