Nothing is written in stone, everything is modifiable.
That said you better be sure to know the biases of the family psychologists in your area. Wrong choice, and the evaluation will turn against you. Remember that both parents are subject to scrutiny.
The costs of evaluation are usually split, say $3000. But the legal work to push or defend is even more costly in trial.
Fathers should NOT have to spend lots of money to justifiably spend quality time with their children. The system is economically biased against dads without surplus cash.