Here is the item again:
Sylvia carefully ironed her one good suit to wear to the bank interview
the next day all the while, Buster, her hairy
white cat, waited for her to lay the dark gray skirt on the bed so that
he would have a warm spot to nap.
Sylvia carefully ironed her one good suit ... is a main clause. Another main clause is all the while, Buster waited for her to lay the dark gray skirt on the bed. These two main clauses can each stand alone as complete sentences, so they require an appropriate break between them.
A period after day and a capital A for all would fix the problem nicely.