Firstly, I want to say that it’s wonderful that you are a Christian, because God’s steadfast love is better than life (Ps 63).
Ephesians 1:3-14 gives a great run-down on what the purpose of our lives as Christians is. God has primarily created us to be in relationship with him. He has done this, not because he needs our love, but out of the abundance of his love for us. He shows us his love in the many blessings that he gives us on a daily basis (which may seem hard to see sometimes), but mostly in the gift of his son, Jesus, whose life, death and resurrection brought us the promises of forgiveness and inheritance. We show our love in return by trusting in his promises (faith) and obeying his commands (living lives worthy of our calling- Eph 4:1).
A life lived in faith and obedience looks different for different people according to their circumstances. Unchanging, though, is our primary commitment to a relationship with God. This will generally be expressed in meeting God over his word (the bible), prayer and trying to live the sort of lives that bring glory and honour to his name.
We all live within the context of what I call “relational responsibilities” - that is we all have relationships that we have responsibility for. Some relationships are more important than others. So in your case, being married, your most important relationship (apart from God) is with your wife; your responsibility is to love her and lead her in her relationship with God and with you. Of course, after her come your daughters - you are responsible to protect them, nuture them and teach them to love and follow and follow Jesus. Our value is found in these relationships, most especially with God, not in what we do.
The key to these relationships if faithfulness. Just as God is faithful in all his realtionships and responsibilities, so he requires us to be faithful to the responsibilites we find ourselves with. This is our purpose, the task that God has set us. He is glorified by our resolve to trust him and do what is right no matter what the circumstances we find ourselves in.
And here is where it gets difficult because sometimes the circumstances we find ourselves in can be pretty awful particularly in our busy high powered western world. Sometimes our circumstances are such that our faith and resolve is tested and “proved”. This is all part of God’s plan to strengthen you and help you - its a sign of his love for you (see 1 Peter 1:3-12 and Heb 12:1-13). Many Christians think of this “suffering” in terms of persecution but suffering can be simply coping with the difficulties that our circumstances throw up. How we face these difficulties will stengthen (or weaken) our faith in God. It is in this nitty gritty of life that our faith is proved and that God is ultimately glorified.
In your situation to love your family is to protect and provide for them. Your job is not an end in itself (however enjoyable some may find their work), but as a means to an end and your responsibility to your employer is not more important than your responsibility to your family. If your particular job gets in the way of these higher priorities, it may be that you need to think of how to change your work situation, either within the job you have or by moving on. Now, I understand this could be really difficult but it may be that this is where your faith in God is to be tested. It would take lots of prayer, an assessment of your work duties and looking at what your family really needs (rather than really wants). It may even mean that you need to make a change without knowing what the outcome will be. This can be a scary prospect!
It may also mean pulling back from ministry in church. Your responsibility to yourself, your wife and family are more important to your responsibility to your church. God would not be pleased if you sacrificed your family because of ministry in church. If he wants to he can raise up others to take your place. It may also be a great example to other men in your church (who are in the same circumstances as you) to see you make godly decisions in favour of your family.
However no matter what your circumstances, no matter what happens, no matter what decision you make, you an be assured of God love and his presence with you. He loves you and your family more than you can possibly know. He can and does bring good out of every situation for those who love him and nothing can stop him from doing it (Rom 8:28-39). So hang in there and keep on doing what is right.
Now I’m not a psychologist, but from my observations, depression seems to fall into two main types. The first is from a trial of some kind (e.g. grief, excess stress, etc.) and once that situation is resolved (grief processed, stressor removed, etc.) then the depression gradually lifts. The second is a longer-term depression that may have the need for on-going counseling to combat unhelpful styles of thinking and also often requires medication for chemical imbalances in the brain. It’s not so black and white in that if people are depressed from a trial for long enough the brain can essentially re-wire itself to become a ‘sad brain’. It might be helpful for you, either way, to seek out a Christian counselor to help you understand where you are at in this regard. (Your minister may be able to advise you).
When we go through low times (for some this extends for life), we are often tempted to doubt God’s love for us. We have to keep praying and remembering we are broken people living in a broken world. It’s not until Christ returns that God will wipe away all our tears (Rev 21:4). Times of depression and trial can also be used by God to draw us closer to him and help us to depend more on him to meet our needs. By this I mean our real needs, rather than what our worldliness often flags as ‘real needs’. (Ultimately our real needs are met in Christ). We learn that we are not in control, but must remember that God is, and he is a loving and compassionate God. The depth of his love is shown in the sacrifice of his son on the cross on our behalf.
As you walk this path, it’s helpful to remember that in many of the Psalms David wrestled with God when in despair, and we can too. Pray to God and tell him of the things that trouble you. Reading and praying through these Psalms can be very helpful. I particularly like Psalm 143. Psalm 13 is also really good and there are many others that are relevant and easy to relate to when feeling down. (Our enemy can be read as arising from within us as well as from without). Be persistent in your prayers because God is listening, but his wisdom and timing are not always ours and we need to trust in him."And we know that in all things God works for the good of those who love him"." (Rom 8:28).
I hope and pray that this is useful to you and that God will draw you closer to him in whatever you are experiencing. Also, I pray that God will work in you, helping you to make wise decisions about what to do with your work situation and seeking further help for your melancholic depression.