Put the baby in your room.
Problem solved.
To artificially sleep train a child/baby just because they are sharing a room... will not work.
They are a baby and a 3 year old. Different age phases and sleep tweaks and baby still needs feedings and will wake/fuss/cry no matter what.
Just separate them.
Baby in your room.... until older and more mature biologically to then sleep better....
Our son, was in his crib, in our room.... until 3 years old.
We have lack of space too.
We have wood floors that creak. Too.
My kids share a space, to sleep.... a revised room that we made into a 'bedroom' for them. They now have their own beds. But this was not until they were older.
the baby, should still be in a crib, in your room. To me. And then, your 3 year old can get a better sleep. A tired or sleep deprived toddler..... will not fare well. At all. In the long run.
And a baby... just due to a baby's nature.... WILL wake and need to feed and make noises. It can't be helped.
all the best,
Susan