S.H.
Try using a "sleep sack" with her.
Look on Amazon. They have it for all age babies.
She may need still to feel cocooned.
Many babies however, once they feel put down in bed, will 'wake' screaming. Because they do not feel your body n or it warmth nor can they sense you.
Also, many babies, do not like to sleep in cribs. Because it is a vast open space. Thus, try a sleep-sack for your baby.
Just try it.
It worked for my daughter.
Also, ALWAYS feed/nurse her before bed/nap.
If your baby is hungry, they will wake and wake a lot.
My kids even cluster-fed, and fed every single darn hour.
And they woke whenever hungry.
Thus, feeding on-demand.
Always.
And yes, babies fall asleep at the bottle or breast, because their tummy is full. Mostly all babies, do this. Its fine. Nothing wrong with that.
Also, if she still has her 'startle reflex' this will wake her too. The startle reflex is an involuntary reflex... which will startle them awake because an infant has no control over their motor-skills nor appendages.
ALSO, have you considered that she is having Gas?
Try Mylicon Infant Gas Drops.
Gas also wakes a baby. And is very common.
Also, some babies naturally go through various stages of sleep. AND they do, make noises or toss and turn while sleeping. This does not mean, they have woken up. They are just, moving around while they sleep. Just like an adult. So, if this is what your baby does... there is no need to intervene or interrupt her sleep rhythms. Because doing so will wake her up.
Also, you need to teach your 3 year old, the routines for him and for baby. My daughter was 3 years old when I had my second child. I always always always, explained to her about babies, about her routines, about her baby brother's routines etc. And when her baby brother napped in the afternoon, so did she. And so did I. Everyday, my eldest KNEW the routines of the day. And, when napping, my daughter was taught to use her 'whisper' voice. And to tip-toe etc.
The thing is, the activity going on while a baby naps, can wake them.
A toilet flushing down the hall, for example, would wake my daughter to a screaming fit, when she was a baby.
She was very sensitive to noises. She could hear a pin drop, down the hall.
With 2 kids, it s doable.
But you need to teach your eldest, about the daily routine. When I would put my 2nd child to nap, I would put things on my daughter's art and activity table. She would be in the adjacent room, but I would explain that while I am putting baby to nap, she needs to be quiet. That baby is going to nap etc. And she knew, that at that time... IF she needed me... to tip-toe and come to me and whisper. She more than understood.
Also, per your surgery, you just NEED to get help. And have another adult around to help you.
Where is your Husband in all this?
Can't he help with your eldest child?
So you can concentrate on baby?
There is no reason, per your surgery, you have to do everything. Still.
I would try the sleep-sack and some white noise.
I always turn a fan on low, when my kids are napping. For example.
But also, you can't make a baby nap longer. Unless you know their stages and rhythms. Some babies, just fuss a lot before sleeping. Like some adults. Toss and turn. My son, would have this monotone sort of sound he made before he actually drifted off to sleep. And he'd toss and turn. But that was HIS routine, HIS way of drifting off. It is a 'self-soothing' manner that he did. I KNEW that about him. Thus, I did not interfere or interrupt that. Because otherwise, "I" would be waking him.
Babies also, cannot sleep if they are over-tired or,
over-stimulated.
Maybe, before nap or bed, the lights are too bright or too much noise.
Who knows.
But a baby will nap, as long as they will.
IF your baby is waking up well and bright-eyed and happy... THEN she had a nap that was long enough for her.
BUT if she is waking up fussy and tired still, then, her nap was not long enough.
Where do you put her down for naps?
It needs to be, in the SAME place everyday. A routine about it.
In her crib or wherever she sleeps.
My kids for example: were NOT "portable" nappers. Meaning, they would not not not ever, nap or sleep while in a stroller or in a car or anywhere. They would ONLY nap, while at home, and in their crib.
But ultimately... a baby will nap if/when tired. And they will nap as long as THEY need to.
You cannot make her, nap or sleep longer.
At this age as well, you cannot make her, fall asleep on her own. She is real young. They don't even have control over their motor movements yet or appendages or reactions.
They do not do things, at-will, at this age.