So let me make sure I have the basics right here.
The couple are separated but living at the same address.
Has this arrangement been in place for at least one year?
Is there documentary evidence to support this living arrangement? Separate bank accounts for example.
Have they discussed arrangements in regards to the family home, pensions, child maintenance?
Is the partner in employment?
Is there medical or other evidence (police reports for example) to prove that he is not a fit parent? Has he been violent? Has he been arrested? Criminal convictions? Proven illegal drug use?
For one parent to be given sole custody of children, generally requires the other parent to be declared unfit, and it is, rightly, a very high bar.
The most usual arrangement (all other things being equal) is that parents are granted joint custody with one parent being the primary day to day carer.
So your friends choices are
1. Do nothing, continue as they are.
2. Start talking, go to mediation, try to come to an agreement. Once you have agreement, this can be written up into a JS
3. Apply for a JS and let judge decide.