Hello and welcome! Firstly, congratulations on the new addition to your family! Here at BW we have a great supportive community, however we do not support CIO in any way because we believe it breaks the bond of trust between parent and child. We are more than happy to help you and your DD get onto a great EASY routine using some gentle methods

If you are going in and comforting her that is fantastic, just make sure you are always responding to her 'I need you cries'

I think what is probably happening here is she is getting a little OT and then is fighting sleep, then if you are waking her to feed she is not having a restorative nap and is therefore OT again. At 2 weeks old her A time is only going to be about 40mins if that...not really much more than a feed and a diaper change then back down for a nap.
Where is she currently napping? Is she swaddled? It sounds like you are trying to have her sleep independently and self settle which is great, but she just might need a little help. Have you ever heard of the concept of the 4th trimester? It basically says that the first few weeks of life are like the 4th trimester, so your LO has always been rocked and swayed to sleep in utero, so when they arrive it is no wonder they can't put themselves to sleep on a flat surface that isn't moving. Many people find that using a sling or carrier in the first few weeks is beneficial until they get a handle on life with 2 LOs and see an EAS pattern start to develop. Alternatively, when you lay her down can you try placing a hand on her or patting her until she's in a deeper sleep? I have an almost 4yr old and a 3 month old too so I know this can be hard, however can you set your DS up with an activity or even a show to watch for a few mins while you help your DD to fall asleep?
The first few weeks are so precious so don't feel like you need to get this right from the get-go. We all do whatever we need to for the first while until things become more predictable around 8 weeks. Nothing that happens between now and then can't be undone
