Is it permissible for a couple to agree to divorce in exchange for the wife’s commitment to financially support the children and provide housing for them, while legal guardianship remains with the father, and is this agreement considered valid শরীয়াহ-wise and legally?

The father's condition that his wife spend on their child and their home is invalid. The responsibility for the children's expenses falls upon the father as long as they are in need, and the wife's maintenance and housing are his responsibility as long as she is under his marital protection, unless the wife voluntarily contributes to that of her own free will.