I imagine that as you refer to your neighbour as "the neighbour from hell", that it is more likely at present that hell will freeze over before you will take round a bottle of whisky, christmas card, or any other sign of goodwill.
There are some people that - now matter how much you bend over backwards, they will never change and even get worse as they take advantage of your apparent weakness.
However - if you think that there is even the slightest chance of winning her over with seasonal good cheer, however much it might choke you to do it, then it has to be worth a try. That way you can also feel superior to her as you haven't sunk to her level of nastiness, and you might even make her feel guilty for her attitude.
You've nothing to lose by giving it a go. But if she remains unpleasant and unhelpful, then my advice would be to ignore her. Tell the planners that you only park in your field gateway in relation to the use of your field. Even point out that you have a driveway to the house, so why would you park over the road? You will then find they do nothing unless she complains again, as they will have ticked the "investigate" box and are not paid to go further without reason.
Should she keep on, then they have to prove why you are parking in your field gateway. That is, in reality, very difficult, without a council official parking up and watching you - which I'm sure you would spot. You can ensure you always leave something small in your car permanently, such as a headcollar, some wormer, a small bucket of feed etc. that you were dropping off at the field. I honestly don't think they'll bother further and will get fed up of her. Planners get nutcases wasting their time constantly.
In the unlikely event they decide to threaten you with enforcement, they will warn you first, and even then you have the right to appeal and that normally costs the planners if they lose. (Which they well could if you keep up the scenario of only parking there to visit your field.) They don't just take you to court with no options for you to justify your actions. Trust me - it is fairly easy to play the inherent inaction of officials. All they have to do is prove they have investigated a compaint, and (unless you are unlucky) they are normally loathe to go further without significant reason.
And lastly, if she keeps on complaining then go to the police and complain of harrassment. She has to have done an action at least twice for it to be harrassment (so that's covered) They may be unwilling to do anything, but persevere and explain that it is spoiling the quiet enjoyment of your property, so is against your Human Rights (look up which one) and is likely to cause a breach of the peace. They won't want to fill in the paperwork so tell them you would be happy if they just contacted Mrs Nasty and asked her to lay off. I have found an unofficial visit by the police incredibly helpful in a case like this.
Good luck.