Though it hasn't been publicly addressed before (at least, not that I can recall), I consider Tribe of Judah a ministry. It is not intended to replace the fellowship, teaching, and worship found in a local church; it is intended to supplement activity in a local church and help members develop a personal relationship with God. Whether tithes should be given exclusively to the church, I can not say with authority; however, I would not feel comfortable accepting a donation from a Tribe of Judah member who attends a local church but does not give their tithe to that church.
While many members in Tribe of Judah attend a local church, some do not. I recognize that, for some, this community helps them build up the courage to start attending or return to a church. Different people are at different points in their lives. Living in Tulsa, I saw a nasty tendency for people to judge Christians who were not attending church rather than open a dialogue and discuss the purpose of the local church. I even found myself exhibiting the same self-righteous and judgmental attitude toward the people I loved. I strongly believe that every Christian should seek, find, and get involved in a local church, but don't immediately assume that someone not attending a local church has given up on God.
There is a nasty tendency in humans to get caught up in legalism. Though the Bible does contain complex passages, most Scripture is very clear and straightforward. Read the Bible, specifically passages on tithing. Pray and ask what the Lord would have you give. If you don't receive an immediate answer or remain unsure of what to do, start by giving ten percent.
Side note: There's also a nasty tendency in the modern church for Christians to show up Sunday morning, drop a check for 10% in the offering plate as it goes by, and feel like they've done their part. The Christian life is so much more.
There are too many Christians who just buy into a guilt trip spouted from the pulpit and feel "bullied" into giving ten percent. What's more important than deciding if ministries are eligible to receive tithes, if you should tithe off net or gross, or if you should give extra for that building program is your personal relationship with Christ.
It's obvious you have a heart after God, so I have no problem trusting that you'll find the answer to your question after reading the Word and praying about the matter with your wife.
And don't worry about ToJ. If the Lord wants us to bring our servers back online, he'll make a way.
My apologies if this post seems incoherent. It's 2:21 a.m. and I should be getting to bed.