Thanks for the question.
This is a difficult matter to address, because it is likely pushing some other buttons for your wife, for which you have no apparent knowledge. So, I would pray for her, perhaps even pray a deliverance prayer, for she could be under attack, and as her husband (the spiritual head of your home,) you have authority to protect and care for her. Don't let satan have any ground in your home. You need to be a warrior in this and deal with the problem at its source. Pray a daily Rosary, bring holy sacramentals into your home, (i.e. prayer and picture sacramentals) and take your role seriously in this regard.
Secondly, to communicate better with your wife on this, try writing a sincere heart felt letter. Start with an apology, for making your wife feel bad, and perhaps even trying to control her. State that your intention was only to partner with her in making the best home possible for yourselves and your children, and that you want to support her in whatever way possible to try to overcome this habit. Say,
"You're right, swearing isn't the most serious issue, but I feel that when we do a good job overcoming some of the smaller things, we'll be even stronger to overcome more difficult and serious things in the road ahead."
But above all, tell her how much you love her and are glad that she is your partner. (You can even mention that if there is anything that you do that bothers her, to let you know, so you can work on it too!)
Marriage is letting God's grace build the two of you up. Avoid conflict, and turn to God when you seem to hit a wall.
This will work out.