Either put baby to bed first, or your older child.
If putting older child to bed first, put baby in the crib for safety.
My daughter was on the cusp of being 4 when I had my 2nd child.
She was patient too. But also still just a young child.
I talked with her often, to bond with her and explain things. She was a champ about it. And tolerant. She understood, that putting her baby brother to bed, was not easy. I always talked with her about it, so she did not feel like a 2nd fiddle.
I was home a lot by myself too, because of my Hubby's work schedule and he is going to school.
Nurse your baby before bed.
Then put him down.
If he wakes when being put down, try patting him etc. use white noise like a fan turned on low. Have the crib comfy and cozy. My son liked baby safe stuffed toys in the crib and we had a Fisher Price "Ocean Wonders" aquarium toy in the crib too. He liked that. It distracts them.
I, put my kids to bed at the same times. Their naps were the SAME too.
Going to bed at 8-9:00pm, is late for a baby and a 3 year old child.
And, over-tired babies and kids... actually have a harder time going to sleep, falling asleep, and staying asleep, and do not get a good sleep.
Have dinner EARLY. Kids, get hungry earlier. Make everything earlier. Their bath, dinner and bedtimes.
If not, the bed 'time'... actually gets later and later, because- as it gets harder to put one to bed, their bedtime gets later and then it domino effects onto the other kid, then their bed 'time' gets later too. A vicious cycle.
So, make everything, earlier.
And, before bedtime... do not have horse-play or anything hyper or noisy. Make the house, DARK and calm and 'boring' before bed. I am talking at least 1 hour before the actual bedtime. You have to set the 'stage' so to speak. Making the ambiance, bedtime... friendly and calmer/darker etc. Leading up to, bed time.
It is a long time to wait, for the older child.
It could also be harder for the baby to fall asleep... because he is being put to bed TOO late. Thereby, you have missed the window of him being tired, and then getting over-tired. Exacerbating the whole process, making it more difficult.