I believe you can transition AND keep your family safe! But, your transition is not going to happen overnight...and it is going to be a long process that requires patience and tolerance of difficult situations. There are many low cost or free ways to BEGIN transitioning, such as a change in clothing, hairstyle, name, and asking people in your life to use the correct pronouns. If you are wanting to be on Testosterone, it is not very expensive, and MAY be covered by your insurance. Even if you pay out of pocket for the T, the lab tests and doctor visits are usually covered. If you have discomfort with the appearance of your chest, you can buy a binder for less than $50. Check with your insurance to see if top surgery would be covered, if that is something you desire. Start saving for surgery, even a little bit at a time. Get started in small ways, and that will lead to more comfort with taking further steps. It sounds like you have great support from your wife, and that you are only stumbling on the financial piece...this is something that CAN be overcome. It may be difficult to see a way through it, but it can be done if transitioning is what will make you feel your best in the world.
