Local authorities, charities and social enterprises are among the organisations that can make a bid to the Challenge Fund.
The fund, from the Reducing Parental Conflict Programme (RPCP), will gather evidence on "what works to reduce parental conflict".
The scheme follows a 2017 Department for Work and Pensions (DWP) policy document stating that better support is needed for families due to the risks to children's life chances.
The resulting evidence will "inform future policy and practice and help local areas support a greater number of disadvantaged families at risk of parental conflict", according to the DWP.
The impact of existing parenting courses is limited if parental relationships are poor, the document also claims.
The money is from the wider £39m RPCP fund, currently being trialled in 30 local authority areas.
- Practice: Respect Young People's Programme
- Parental conflict: the impact for children and how to resolve it
The cash is being made available via two funding streams, with £1.1m for Support for Disadvantaged Families, who are said to be at greater risk of parental conflict.
A second strand, Digital Support for Families, has been allocated £1.6m, to "test what works digitally to support and maintain engagement".
This has a specific focus on targeting parents in low-income families by promoting support via websites and apps they use.
The DWP statement, issued with consultancy Ecorys and the charity Family Lives, says that the funding will "seek learning on what works to support disadvantaged families by funding innovation where there is little current evidence".
"For example, this might include innovation to promote better integration or join-up of local services, or targeted interventions for families."
"We are also interested in innovation which explores how supporting parents to reduce their conflict can reduce the number of parents going to court when they separate.
"As a key aim of this fund is to encourage innovation, we will not fund activity which is already taking place unless there is a strong case for doing so."
Applications open on 21 January and close on 15 February.