Is the mom-cat on the young side? Sometimes young mothers (under a year old) will not know what to do and will need your help and guidance.
She may be moving the kittens because she feels they're not secure in the locations she places them. This is not uncommon. If she wanders away from the kittens and it's not just to eat, drink, eliminate or stretch her legs, but stays away from them for more than about 10 minutes, that's something to be concerned about. The most important thing is that the kittens need to be warm; kittens can't regulate their own body temperature, so laying cuddled next to each other and the mom-cat, supplies that warmth. A chilled kitten cannot metabolize the milk it drinks.
If the kittens ARE getting enough milk and the mom-cat is being attentive and seeing to their needs, each kitten will choose its own nipple for nursing from birth, and will continue to nurse there by seeking out its own scent. It will nurse every two to three hours. A kitten that is thriving will quickly develop a fat tummy and will sleep peacefully. A kitten that is NOT getting enough milk or who may not be warm enough will make a lot of noise (mewing) and move around a lot more than one who is well fed.
I would suggest that you bring the kittens and mom-cat into the upstairs bedroom, to the nesting box you set up (a large cardboard box with the sides neither too high, nor too low, layered with towels) and put her food and water on one side of the room, and her litterbox on the other side, and not allow her free roam of the house at this time until she's into a good routine with the kittens.
She may feel nervous and not like the spot you picked out for her, but as long as it's dimly lit, warm, non-drafty and quiet, it should be fine. I
think if she stays in one place with the kittens, they should all do well. If, after a few days, you see that the kittens ARE nursing well and she's licking them to clean them and also stimulating them to eliminate by licking vigorously at their rear ends, she's taking care of them well. If you feel it may be too chilly in the room they're in, and for the times the mom leaves the nesting box, you can place a heating pad on low, under the layers of towels, on ONE sied, so if the mom gets too warm, she can move off it, to the cooler side.
I'm not implying you should keep her 'prisoner' in that bedroom, but it's very dangerous for her to keep changing their locations as you suspected, and she might place them in a spot which is drafty, cold, or a place you can't get to, to see them in order to monitor their status, and that wouldn't be unsafe. She may need a little encouragement and help from you if she's acting confused, so place the kittens at her nipples to encourage them to nurse and observe them in the bedroom, in the box.
Once they're into a routine and you're sure they're eating well and she's caring for them properly, you can allow her to roam the rest of the house.
Make sure the mom is eating a premium KITTEN food for extra calories while she's nursing.
For more information on newborn kitten care, please see:
If you find they're NOT eating enough, you will have to supplement with KMR (kitten milk replacer), which can be bought at any pet supply store (along with bottles and nipples), and also at Walmart.
If you should have to help your mom-cat with supplemental feedings and stimulating them to eliminate, etc., the following links contain information and instructions on caring for abandoned or orphaned kittens:
A lot of the information is repeated, but they're all good sites for this type of information.
I wish you much good luck and congratulations on your new feline family! Please let me know if I can be of further help.