Please note that the current SNP Government in Scotland has gone extremely quiet about a second Independence referendum - there is a very good reason for that - they know the answer would be a resounding NO. They have not resolved, or formulated answers to any of the "difficult questions" they failed to answer in the run up to the last referendum and with Leave winning the Brexit Referendum it makes answering those questions even more difficult.

Scottish trade is distributed roughly as follows:

15% with the rest of the world (Would remain unaffected by Brexit)
65% with the rest of the UK, primarily England (Would remain unaffected by Brexit)
20% with other EU member states

So economically and socially the Union with the rest of the UK is a damned sight more important to Scotland than any "union" with Europe.

Time lines for a second Scottish Referendum and an Independent Scotland rejoining the EU:

29th March 2017 - Article 50 triggered
29th March 2019 - Brexit negotiations concluded
Summer 2019 - Second Independence Referendum called for and agreed (Last one involved two years of preparation and campaigning)
Summer 2021 - Second Independence Referendum which hypothetically results in a YES vote (The previous timetable for Scotland to divorce itself from the rest of the UK was two years)
Summer 2023 - Scotland becomes and Independent country - it will either have a currency over which it has no control, or it will have to have established it's own brand new currency.
Summer 2023 - Scotland applies for membership of the EU - The EU will look at Scotland to measure suitability and compliance and advise Scotland on what must be achieved before membership can be applied for and for that application to be considered by each member state. (In the case of the Baltic States this process took 15 years)
Summer 2038 - Scotland finds itself an independent country?? and a member of whatever size, shape and form the EU has evolved into by 2038 which could mean that Scotland isn't independent at all.

Both Big Al and Keith A are perfectly correct in what they have said so far. Oh and just as an aside my first trip to Northern Ireland WAS to protect the "nationalist" Catholic population against the Ulster "unionists" and to oversee and ensure the disbanding and disarming of the RUC's B-Specials.