Out of interest, what if the father was dead
If the father is dead then clearly consent is not needed. However, you may be asked to prove he is dead.
The only problem you’ll have is IF his dad finds out you are going and takes you to court to get a prohibitive steps order
Not true. People are refused boarding or refused entry every year without the father getting a Prohibited Steps Order.
A parent can take a child on holiday without the other parents consent, except in some particular countries, ie. South Africa, where a letter is required
Simply not true. The countries that check vary. Indeed, sometimes it depends where you are entering a country or even which immigration officer you get. If you travel without consent or a court order there are no guarantees. You might get away with it, you might not.
of course a mother can take their DC on holiday whether the Father is absent or not! That's not a crime
Yes it is. Child Abduction Act 1984.
I'm sure it can be classed as a crime if the parent absconds, but if the absent parent is dead, disappeared, absent you do not have to have written permission
Not if they are dead, clearly. But, as the law stands, if the parent has disappeared you are still committing an offence by taking your child out of the country, even for a holiday, unless you can show that you have taken all reasonable steps to communicate with the missing parent but have been unable to do so.
Just to repeat, loads of parents break this law every year. But, like it or not, it is the law. On previous threads some parents told of times they had been prevented from boarding or denied entry. That is the risk you take.