YANBU.
It took me three weeks to get about 75% unpacked when I moved with a 6 month old, a 2.5 year old and a 5 year old who was spending 2.5 hours a day in school (in the US where school days can be short for early years). I barely got DD1 packed off to school when I had to go out and pick her up again. DS(2) was into everything -- piles of sorted stuff got mixed up in seconds. The baby crawled around and put everything into her mouth including dirt and god-knows-what that she dug out from under the fridge and cooker (previous owners left the place filthy) and DS's toys.
Babies wanting almost constant attention from mum is not at all abnormal in my experience. I tried a carrier for DD2 but I was doing a lot of leaning over and it wasn't practical. She had started crawling and just cried in the portable sleep-n-play.
DS liked boxes, and DD1 too, and they both liked TV. However I had to take frequent breaks for cooking, feeding, cleaning up after feeding, watering, pottying (DS dry but needed help wiping), changing nappies, answering endless questions 'Why?' from DS, and trying to concentrate was difficult with all of that going on while at the same time keeping an eagle eye out for behaviour of both DS and DD1 with baby DD2. It was a stressful time, and sleepless nights added to it -- DD2 was teething like crazy. The older two liked the TV and played with the boxes, but they squabbled plenty, and they somehow needed endless snacks, spilled drinks, etc. DD2 loved sorting through a basket of odds and ends and I could set her down and let her at it, but invariably she crawled over to me to sort through whatever odds and ends I was dealing with most of the time.
I had no family to help and didn't know any neighbours. After buying the house we didn't have two pennies to rub together so babysitters were out.
I got on with it as much as possible, and everyone lived to tell the tale. But I was exhausted afterwards. This was after I had done all the bloody packing too. exH couldn't be bothered, just liked chivvying people around but was useless with actual contributions to anything that had to be done.
At least we didn't have a cat at that point in my life.