Dear Don 

You can check out with your local diocese, but usually those called to the diaconate have already dedicated themselves to their family, and their children are all grown up. Your pastor should be able to tell you what the conditions and expectations for a deacon in your diocese would be. Your wife's instincts are good: your primary vocation now is to be husband and father, and you should not take on commitments that are going to drag you away from this. This however does not mean you cannot do anything for the Church for the next so many years while you provide for and guide your family. I would recommend that you and your wife both continue to learn more about your faith (catechism, apologetics...), and as your family grows and you cater for your children's needs you simultaneously try to do things that will benefit them and other children of their age - thus doing apostolate. If you would like the name of some apostolic group of Catholic laity that might be able to help you to do this, feel free to get back in touch with me. God bless.