I think you guys do have a dilemma. The kids are too old to share a room. You can't expect a 15 year old to have a baby in their room and you coming in and out for the next year with a baby that wakes up to be fed all the time. Nor can you expect a 12 year old to do it either.
The basement is not an extra bedroom, it's family living space whether she has it as as studio or not. It's not a bedroom or suitable for an infant. Do you have upstairs? So any child you'd put down in the basement would literally be 2 floors away? Even if your bedrooms are on one main floor I agree with you that a basement is not where I'd want any kids to live.
So, do you have a den? Walk in closet that could be modified? That's what a friend of mine did. They had a bonus room at her mom's house and they were living with her parents while rehabbing an auction house they paid cash for. They took the eaves of the attic that were closed off to make a square room and built in a bathroom and a huge closet and an alcove for the baby bed and dresser for the baby. They made it quite well until they moved into their home.
So find space in your home to turn into a baby space. We had the crib in our bedroom for a very long time due to him having reflux and having to sleep sitting up in a bouncy seat. He was strapped in and wasn't turning over yet so he could literally choke to death if he had a reflux episode.
When we went to house sit my mother and father in laws house while they traveled we set up a toddler bed and the baby bed in the guest suite and had both kids in with us.
My best friend for years and years and years was one of 12 kids. There was a boys room, a girls room, and mom and dad's room with all the kids 3 and under in there in baby beds and stuff. They lived like that until all the little kids were big enough to move into their big kids rooms and the big kids started moving out and getting married and stuff.
So there are ways to do this. You just need to think outside the box, the bedroom box. A baby can stay in the room with you, in a baby bed, for at least a year. By then things might change. In a couple-three years the older one will be moving out and off to her adult life. Then your little one can have their own room.