In point of fact, giving explicit permission to someone to use part of your land will never give rise to them being able to claim it by adverse possession : for adverse possession to arise, the neighbour has to be using it as of right.
But, you have grasped the most essential point about boundary /property disputes: that de-escalation is key, and the only guaranteed outcome of invoking the law is that lawyers get richer.
2 difficulties:
Someone who thinks that something is already theirs, so sees you as trying to take it off them
And, someone who jumps to conclusions, and seems incapable of seeing someone else's point of view.
Contesting the points of someone with this mindset is pointless. They will just fight harder.
You have to sidestep.
Eg, they suggest plan from previous owner, don't disagree. Agree that jointly looking at a plan would be a great idea, thank you. Then ignore their suggestion, get the actual Land Registry plan- you'll probably need to enlarge it . First look at any fixed points- eg if the boundary clearly lies at a mid point of the 2 houses, on the plan,it's position can be determined by measurement. Which you will want to check in the first instance when the neighbours are out.
Agree on everything you can, in the face of unreasonableness.
" Yes, this difficult."
"Yes, people may have got it wrong in the past."
"Yes, we need to get this sorted out."
Then present your clear evidence, from the title plan. Be as neutral as you can. 'It looks to me like it's in the middle. What does that look like you ?'
Download their deeds from land registry.
-look at their plan
-check who owns it- if both women do, say that you need to speak to both of them, in the hope the other is more reasonable.
If DH can't/won't button it, suggest he steps back.
Good luck