Now I have about 5 months to get her to change her mind on this or were going to have a seroius disagreement.
You're going about this the wrong way. Your goal shouldn't be to get her to change her mind, it should be to show her why you enjoy sailing like you do and how knowing sailing can enrich the lives of you, her and your kids.
Taking the family away from all the electronics, creature comforts and distractions we now think are an every day part of life and spending some real quality time together is a great goal. Your time together will become much more enjoyable and fulfilling than any time you can spend ashore.
That your wife objects to the expense tells me she's not getting any enjoyment from the boat. Why not? You need to find that out, the real reason, not just the finances. If she's not coming with you when you sail, you need to figure out a way to open her mind to coming. You also have to show her the joys of sailing and that doesn't mean criticize her because she's not seeing it like you are. You can start with a weekend in the harbor and a little putt-putt along the shore at night. Very romantic! Whatever you do, do it slowly and pay attention to how she reacts. Don't force the issue!
If you sail without her, do you ever take the kids? If not, you should. Even if you never leave the harbor, you will enjoy a lot of quality time with them and get them used to the boat. And if they enjoy that time, your wife will see it and maybe be more open to joining you. Even if she doesn't, you will give her some free time to do what she wants while you have the kids. Women appreciate that. Even if she's completely turned off by sailing, she'll recognize the boat as that place you take the kids enabling her to get her R&R.
The boat has to bring her some pleasure or she'll never be able to justify the cost.