Without knowing all the facts, it would seem that the vendors solicitor is probably in negotiations with the neighbours solicitor re the boundary and is probably waiting for this to be resolved. For your sake as future owners of the property your solicitor will require this to be in order too. I take it your solicitor hasn't received the full set of title deeds to date either so hasn't been able to investigate if the issue has been settled.
Would have thought the vendors solicitor should have informed the vendors of the ongoing issue if it is one which arose while they owned the property, unless the vendors solicitor just didn't spot it when the property was originally transferred, or possibly it was something which was started and now since the property is being sold, has to be resolved fully.
Its certainly not good practice to tell her clients (the vendors) that the delay is on your side and fair play to you for calling the vendor directly. I would suggest any action taken is cc'd to the vendors so they are kept up to date with your position.
However now that they know that there is a problem (on their solicitors part and not yours) it is likely that they will put the pressure on to have the issue resolved asap.
Re complaining to the Law Society after the sale has gone through, I'm unsure what way this would benefit you, apart from reporting their slack ways but this is your call. I'm sure the vendors are equally unhappy with the situation especially as they are paying her for the 'service' she is (not) providing. However, she may also be at the mercy of the neighbours solicitors regarding the boundary so it is a catch 22.