Aww, these 1st few weeks must be so hard when you have a toddler too - I honestly don't know know how people manage more than one lo! My lo didn't like his moses basket and had to be really zonked after a good feed before he would settle but like you he would sleep in it quite happily through the day. He also fed non-stop through the night but slowly he started to settle - we realised we had been overheating him as our room is quite warm and we had him done up like a wee christmas present. I was also guilty of putting on the big light when feeding through the night.
I'd suggest you stick your basket, especially if your lo likes it during the day - check temperature and try some of the suggestions from pp. Your lo won't have any idea on night and day yet but that'll come in the next couple of weeks and the darker mornings and evenings - yuk- will help.  Take good care of yourself and maybe see if somebody will take care of your toddler for a few hours and let you just sleep whenever your new baby sleeps.

my dd is 8 weeks and has only been sleeping in the moses basket for about 2weeks. Like you she seemed to want feeding all night and would only settle if she fell asleep feeding. The first few weeks are hard and it does get better. I was given some tips for getting her to settle in the moses basket. You  can try and warm it up with a hot water bottle, put something in it that smells of you. These things didn't work for me and it was only after the 6wk growth spurt that she has been more satisfied with the feeds and easier to settle.

My dd is 2 weeks old and has never slept in the moses basket on a night. During the day she sleeps in it fine but won't settle in it at night. She is breastfed n seems to want feeding constantly in the night. i am so exhausted and have a 2 n half year old to look after during the day so no chance to sleep. Any advice on how to get her to sleep on her own in the moses basket? i've been told to put her to my boob whenever she wants to but she can't need feeding as often as she seems to.