Maybe it's the English/Welsh eurosceptic in me, but I don't agree at all that all EU nations have equal power. In fact, that very much isn't the case. The eurozone crisis shows just how much power the central core of the EU can have over its member states. All member states have equal power in theory, but at the end of the day, the core of the EU is built around the Franco-German friendship/agenda and the core of that is, essentially, a German driven agenda for Europe. Germany, the most populous part of the EU is akin to England in your perception of the UK. I think Scotland will make a large mistake to destroy the nation its a part of the join the EU, where it'll be a small speck amongst the wider EU.
I completely agree, however, that the UK is not a union of equals. However ask anyone in England and they will agree with you too. English voices have been ignored for a long time, hence Brexit or the collapse of the Labour vote in December. This is a result of an organically growing nation over the course over 300 years. England is not a place of immense power and smugness from being the dominant player in the UK-far from it. It has as much discontent as Scotland. In fact, I'd argue even more discontent, seeing as the Scots with a devolved government at least have a bit more power for themselves. England has nothing like that-and is sick to death of the same politcs it's been getting for decades. This dosen't mean, as the SNP portray, that the UK is intrinsically undesirable, but does suggest the country is overipe for an updated political system.
I don't think it needs a formal constitution or terms of membership, because it's not a group, but a Union of crowns-which is a concept that admittedly is quite abstract these days. Scotland has far more latent weight in the UK, because if Scotland leaves the UK-the UK ends. If the UK leaves the EU-the EU continues with virtually no change on the outside. Having the ability to essentially destroy the country if discontent is strong enough is an incredibly strong position. Similarly, London, the economic centre (for better or for worse) of the UK has much potential weight. Yet our trains still don't get the investment it needs and our housing makes it impossible for a normal family to start a life here. Seperation is not the answer, but perhaps different kinds of decentralisation is.