how to sleep train with another LO in the same room

I have a 7 month old and a 2 year old. My 2 year old has always had trouble sleeping and has only recently started sleeping through the night about 75% of the time, but she doesn’t go to bed until late. I She shares a room with my 7 month old, who as a newborn pretty much slept through the night no problem and was such a good sleeper until about a month ago when teething started. My toddler is a fight to get to bed and usually goes down around 10 or 11 after so much coercion. The baby wakes up hourly or more at this point to be held or nursed or whatever and his screams are so persistent. I didn’t sleep train her because I don’t believe in it but for the first time I really dgaf about my beliefs because I have not slept in so long that I literally am having extreme violent thoughts towards the baby, but because they share a room I can’t really let him cry it out I just have to give him what he wants so she can sleep. And if she comes to sleep in my bed it doesn’t make much of a difference because the rooms are close and he’s so loud so she starts crying because she wants me to help him. I don’t know what to do but I know that if I don’t figure it out soon baby will not be safe. I do have help as we live with my mom but I’m pretty sure we’re all getting to the same point