The woman and her female partner have instructed their lawyers to fight the man's demands on the basis he has 'betrayed' a 'pact' the threesome made before the baby was conceived, in which they allegedly agreed he would have 'limited' parental rights.
The parents are not being named in order to protect the little boy's identity, but are reportedly all highly-paid professionals living in central London.
The father is said to have attended the baby's birth and currently has five hours of contact a fortnight with him. He claims he was always more than just a sperm donor, and now wants the right to have a full parenting role in his son's life.
The Appeal Court heard that the man had been 'utterly consistent' in his desire to parent the little boy, and gained 'pleasure and joy' from interacting with his son.
The child's mum, however, says they had a 'clearly agreed' pact with the man before the baby was even conceived, which stated she and her female partner would be the 'primary parents' within a 'two-parent, nuclear family'.
The court heard that the man was previously in a marriage of convenience with the woman which ended in divorce.
The Appeal Court judges are now being asked to rule whether the toddler would the better off with 'three parents and two homes'.
The lawyer for the mum and her partner said the couple had been left with 'bitterness and betrayal' and would have used an anonymous sperm donor if they had known the dad would take this stance.
Charles Howard QC, told the court: "Notwithstanding their sexuality and that they acknowledge to that extent that they are an alternative family, the mother and her partner hold very traditional views of family life and would not have chosen to bring a child into anything other than an intact, two-parent, family.
"The ideal upbringing for a child is a stable home in which the parents love each other and had together chosen to bring a child into the world. This is the upbringing which the mother and her partner always wanted to create for this little boy. They were always of the view that their son's best interests militated against him spending very much time away from them or from his home.
"The intention was always that the father, who was at one time their close friend, would generally see the boy in their company by sharing in activities and family events. The breakdown of the friendship has had the result that the boy is spending far more time away from his primary parents than they had anticipated."
"To this couple, the concept of 'three parents, two homes' repeated so often by the father, is very alien and has never been something they could consider. This is something which they have had to accept but it represents a significant departure from their initial plans for their son's upbringing. They cannot conceive of their child being shuttled, physically but more significantly emotionally, between two homes and it is something that they believe will harm their son and cause significant emotional damage."
The dad's lawyer said his client had no desire to undermine the role of the mum and her partner as the child's primary carers, but wants sufficient contact with the toddler to enable a 'developing relationship' with his only son.
What a messy situation!