dont worry, its completely normal. 2 month olds rarely sleep thru the night but to be honest, 3-4 hour stretches is pretty good. the definition of a baby sleeping thru the night is 5 hours straight, so if a baby slept thru midnight to 5, thats considered thru the night for a baby. if you get 4 hours at times, your doing pretty good as that at least sounds like he knows when nighttime actually is.
for the nap thing, im going to tell you two completely contradicting things. napping actually helps babies sleep better. overtired is the absolute worse thing for a baby, far harder than even a hungry baby. try to get to the baby before he is overtired. baby wakes up, feed him. then play with him, then after he is up for 2 hours, time for a nap. 3 solid naps is what i got around this age. remember eat play sleep during the day. if your baby sleeps well in a bouncy seat, just do it. get thru these first difficult months, and later work on the transition. my 2nd daughter hates to sleep on her back during the day. i tried everything. at night she was fine, but in the day would wake up after 5 mins. i still put her in a bouncy seat now at 8 months. its not vibrating or anything, she just likes that position.
now for daughter number 1, she never napped. 20 mins naps in the beginning, and 45 min naps when she got older(while everyone else talked about 2-3 hours for their babies). she slept pretty good at night but more so at the 3 month mark. we cosleep which greatly reduces the amount of actual wakenings during night. we had added up all the time and she was far below the averages in total sleep time. we stopped worrying about it. everyone agrees if all functions are normal, and the baby is happy when she wakes up, and not cranky all day, she is getting enough. this baby was exceptionally alert, even at birth and in the hospital, several doctors and nurses commented on how alert she is. to this day, she rises at 7 am whether she goes to sleep at 7:30 or 9:30.
for the night, just make sure you try to get to him to feed him before he is actually awake. i find doing this, my daughter goes right back to sleep. never turn on the lights, and when you can, dont change the diaper everytime if he wakes up. make sure he is eating a full feeding, he may be falling asleep before he has eaten enough.
dont set a schedule for your baby, he is too young, at only 2 months, its great that you have gotten him to sleep during the night hours and be awake during the day. he is taking in so much and his little body is trying to adjust the best he can. stay away from babywise. that book was written by a pastor with no medical experience whatsoever, its like asking the garbage man for advice. you should never in any way direct feedings, babies need to eat when they are hungry, and every child is different in terms of how they eat. my one daughter is a snacker who eats 5 mins every 2 hours, the first downed every last drop and then was good for 3-4. all babies are different so you cant schedule how a baby is. you are to follow his schedule he shows you, not the other way around. just remember the eat, play, sleep(after 2 hours) and see if that helps. adjust the time awake if needed.
as far as where he sleeps, make whatever changes you need to for him to sleep well. maybe look into that wedge that is used to give an incline. just check the age recommendations. i would def wonder if reflux was an issue as discomfort when laying down is a red flag. def talk to your doctor about that to go over the symptoms in more detail.
also try swaddling(completely or partially), white noise, and pacifiers(at this age it should be ok if you milk supply is good). dont stress too much and dont allow your baby to cry it out if anyone suggests that. it teaches nothing, only that a baby passes out from exhaustion. he is crying only for his needs to be met. some babies dont sleep thru the night for several months(mine is 8 months and doesnt but my 3 year old did around 6-7 months). and dont always believe people who may tell you their baby does. eveyrones idea of "thru the night" is different or what classifies "waking up". your son is going to change so much this year. everytime you think you have it figured out, it will get turned upside down. with illnesses, growth spurts, teething, learning new things, ect, there is going to be lots of changes for his schedule. at this point, let him set his schedule, and follow it. until you go back to work, make sure you take naps when he naps, or go to sleep earlier to help. also, one thing you realize with a second baby, there really isnt a reason why 2 people should get up in the middle of the night when a baby wakes. im not sure if the baby just wakes everyone up, otherwise, having just the person feeding the baby really helps.
i know i didnt give you any magic solution, but i hope something helps. i know its hard but it will get better. good luck to you.