Hi Nayla! As you saw in this thread, this situation happens now and then. "Just swelling or a kitten left??" Or even - we know there IS a kitten left... The answer how hurry it is, is if the mom seems ok, calm, happily busying herself with that already delivered kittens - do observe, but you can wait.
If the mom is visibly in difficulties - you must contact a vet, and be ready to rush in.
Likewise, if the mom comes into labor and it is a long fruitless labor, say max 1 hour... The labor of kitten nr 1 may be several hours, the labor of following kittens shall be shorter.
So my advice for you is, if she seems OK, you can wait till the vet open. But when the vet opens, do contact your vet and hear his advice. With such a very big, deformed kitten, the mom may need some vet attention, even if it is not hurry with the last kitten, or it is just swellings. So be prepared to take her in.
Your mom has right, if there is a dead kitten inside, and it dont goes out by itself, a vet must help you. It is usually not crash emergency hanging on hours, but must be done very soon before they decay and rotten.
So, contact your vet as soon as he opens. If it takes long to open- phone at least, otherwise you should take her to the emergency vet anyway.
I hope my answer helped you.