Hi!
I also have 2DD. Slightly different ages than yours. DD1 is 3 and DD2 is 6 months.
In total honesty I find two children hard. Don't get me wrong, I love the bones of their little bodies but I find it quite a juggle.
I am still on maternity leave and subsequently I have both DD's all the time. We are very fortunate as when I work our childcare is Grandparents. So being off means I have two all the time.
DD1 is a little Angel, she is funny and chatty and a superstar when it comes to sleep. However she is PFB. She had ALL of mine and DH attention. We adore her (still do) but because of this she has been a challenge when I need to do something with DD2. Quite often says 'Put DD down'
DD2, she is my little smiler. Such a little heartbreaker when she giggles. But, like your DD2 she lacks the sleep gene. I can't breathe wrong when she is down and she will be bright eyed and bushy tailed.
When she does sleep, DD1 will decide that is the time to play wooden blocks and bang the floor (I scream inwardly EVERYTIME)
I have learned to cope with the sleep with DD2. I honestly don't feel as tired/ratty.
However the dynamic of two is different.
I am learning to do a few more things with both, this brings me much more enjoyment. Now DD2 is sitting up, DD1 can interact a lot more. I ask DD1 to give DD2 toys etc.
I also have done a few KIT days in work. I have loved those days. The girls were well looked after and when I came home we have had a wonderful afternoon.
In answer to your question (sorry for the long post) I don't feel like a natural parent, I second guess myself. I see photos on social media and all the kids seem to be loving life, where as I feel I am purely keeping two people alive (yah me).
The sleep deprivation does get easier, once that happens I think you will enjoy more xx