Here's a previous thread with some similar discussion.
Keep in mind that the "Suzy Homemaker" image was largely a creation of advertising -- real housewives tended to be considerably less glamorous than the people seen on TV or in magazine ads. I recommend Stephanie Koontz's book "The Way We Never Were" as an excellent discussion of how mid-century families really lived.
As for access to money, joint bank accounts were common in the thirties, let alone the fifties. Most households worked on a budget, and it was generally the wife who was in charge of administering it -- she might allow her husband a certain amount each week for walking-around money, but in general she controlled the family pursestrings. He would turn his check over to her on payday and she'd run things from there on.
A housedress is a cheap, simple, often homemade cotton calico dress with buttons or a zipper up the front for easy donning. It was usually worn with low-heeled oxford-style leather shoes and either cotton stockings or ankle socks. Hair would often be up in a headrag, tied over curlers. The typical woman wouldn't go into town dressed like this, but she'd have no problem going out in the yard to hang up the washing so attired.
A girdle would generally be worn if only to hold up the stockings, but many women found the back support helpful while doing housework. If the woman had had several children the abdominal support was also welcomed. The bra would generally be simple cotton with structured but not exaggerated cups and elastic inserts along the band. Slips would usually be worn to keep perspiration away from the dress -- a simple cotton slip for everyday and something fancier in nylon or rayon for dressy occasions. Cotton briefs or wide-legged tap pants would be worn over the girdle, not under it.
There was plenty of work to do during the day -- washing, ironing, dishes, vacuuming, getting groceries, food preparation, figuring the budget, paying bills, etc. It was not uncommon for a woman without kids to have a part-time job of some kind, especially if the couple was young and just starting out.