I'm so sorry Mama. That sounds frustrating. I have an 8-week old baby, who can also be difficult to lay down for a nap sometimes. We have made some strides in this area due to a couple things. We always swaddle her for sleeping no matter what. We use one of those special swaddling blankets and it works like a charm. We also have been using a white noise machine next to the bed. I also think she sleeps better if I nurse her lying down on the bed, then I don't have to move her after she falls asleep.
Also how long does it take to put your ds to sleep? Is it possible for the baby to lay awake in a bassinet while you put your older child to sleep. In the recent weeks if we need to get something done, we've been putting our baby in her bassinet awake and letting her hang out as long as she's happy. I think it's relaxing for her as long as i don't do it too often.
If none of these ideas help, maybe you could get help from a friend, relative, or neighbor. Or you could hire a mother's helper. Someone who could come over and hold the baby just for the time it would take to get your older child to sleep. This doesn't have to be a permanent solution. As your baby gets older I'm sure she'll be able to handle being put down for longer periods of time.
Jennifer, mama to darling dancing Juliette, and sweet baby Jameson