There is a saying Act in Haste, repent at leisure.
I think that you have got very good advice on this thread from people who have been through the mill on property sales.
The problem, as I see it, is not obviously caused by one party. Your vendor has probably been economical with the truth and you have paid more for a house than you should have done if all the facts were known.
The neighbours are pushy to say the least and more than willing to stamp all over your rights as a neighbour - no matter how nice they are to you to your face they are still pushing on with their plans and actually want to get going quicker than the legal requirement.
And your solicitor looks to have dropped the ball - I think a good solicitor would have sniffed this issue out.
I think that you should take on all three for the issues identified - I know this is not easy - it's not something I am good at either - but you nearly need to force yourself to play hardball with each - you will get more respect.
There is a strong chance that you will regret letting this all go ahead without ensuring your rights are protected / get recompence - I also understand your concern regarding your own buyers but that is what happens in the property game - don't push yourself into years of regret and never totally accept the new house. It's your hard money going into this - why should the vendor / neighbour/ solicitor gain at your expense?
That call to the litigator solicitor should be d9ne asap. Also, Don you know anyone experienced in property purchases / sales in real life? A relative, friend, friend of a friend, work colleague? I think that you really need someone that knows about this stuff in real life to give you some advice / backup.