Hi hun - well, I have two and my younger one did exactly as you described with naps getting more difficult when wearing her. So I do kind of have some btdt experience, but we were in the weird position of moving countries when DD2 was born, so we spent some time living with both sets of grandparents and I had extra hands for settling the baby or playing with my older one. By the time we got sorted in our own place DD2 could settle herself. But she did a lot of short naps, so I do understand having a tired crying baby and a bored older one. Will your baby sleep in the car seat or buggy? Mine is a pest and doesn't really do that, but if yours does I would make the most of it and get out with DD1, run errands etc and let DD2 sleep. That's one nap you don't have to stress about, and as long as you're not doing it all the time it shouldn't affect her ability to become an independent sleeper.
I hate to say it, but in the beginning when I was home alone with both of them the tv helped a lot. DD1 watched more than usual but there's only so much you can do when there's one of you and two if them, yk?
Is DD1 home all the time? Just wondering about preschool or anything like that. It was very helpful to me to have my older one out the house for 2.5 days a week. That sounds a bit mean, it was obviously not to be rid of her, but just a relief to know that I could focus on the baby and naps without interruption during that time.