Where exactly are you up to in the process, OP? What is left to do?
We had a loft conversion done that dragged on for 6months in the end - our DD wasnt a newborn, but was 10months and crawling and trying to get into everything, which we didnt think about when we started it when she was so little!
We moved our bedroom downstairs into the lounge to be as far away from the work as possible. We didnt have another child at that point, but if there's space for the toddler as well, id say just have you all sleeping in one room. Newborns are sleepy to start with and if your toddler is a good sleeper they might sleep through the baby waking anyway.
We put a lot of furniture / boxes into a storage unit to give us a bit more space. They often have offers if you book for a set period so you could book for 2months, get a man with a van to move stuff for you, put sofas in the unit, set up a bed downstairs, then you can be comfy and camp out so the toddler can play. It will be cheaper than an airbnb. Don't stress about tv - let them watch whatever with you just to get through this periods. It will only be a few more weeks. I bought a snoozeband so I could watch tv through my phone whilst DD was asleep in bed.
Its a very challenging time anyway when a second baby comes home and there's a lot of figuring out routines, change for the big one etc. If they are not in nursery FT, id also consider putting them in FT so you arent worried about cooking for them / midday naps etc. FT nursery was a godsend for me when DD2 came home because it meant I had 7hrs in the day to just deal with one child, recover etc.
It will be worth it in the long run - our loft conversion has been amazingly beneficial to our life, and you are in the worst part of it right now.