Luisa, EU law is superior to national law, in Europe. The situation is analogous to the individual States in the USA. Europe is now in theory a federal state, with countries following EU law. Where there is a conflict between national law and EU law, the EU law is superior; if the country fails to enforce the EU version then it has to pay fines.
Regarding the financial stability of EU countries, there are a number of weak currencies/countries but the majority are stable. The EU should not be confused with the Euro, a currency unit used by some EU member states. The Euro is fundamentally flawed and has numerous significant issues, principally that there is no exit procedure for countries that have collapsed either politically or financially, leading to a devaluation situation that cannot be resolved since they are members of an external currency group.
There is a link between the Euro and the EU but it isn't relevant to discussion of EU law. EU law applies to all 27 EU member states, far fewer are in the Euro. There are many very solid countries in the EU and some are also in the Euro.
The principal issue in Europe currently is that there are about 30 countries who will do anything - no matter how unpalatable it is - to maintain and strengthen a pan-Europe bond that prevents war. In Europe there has been almost constant war for the last thousand years, and people are finally tired of it, the last one was the clincher. The only solution to that is seen as a federal state that will act against any member starting a war. This is the unspoken reason behind the EU. The problem, in practice, is that the EU 'government' is unelected and answerable to no one, and has the usual incompetence and corruption problems to be expected. Nevertheless people tend to want to keep it despite the problems.
Unless you have experienced a modern war in your own country you cannot possibly have any comprehension of this issue. Modern wars are totally destructive and the experience of the last two in Europe has convinced people that absolutely anything is better than that. The EU is the result. It has major faults but most people would probably vote to keep it, despite the fact that, the way it is going, the harm it does is growing by the year. Corruption is the main issue and looks to be incurable. As an example, the EU health committee has been bought by pharma and their EU-wide Snus ban kills somewhere between 70,000 and 140,000 EU citizens a year, by my estimation. But people are OK with that because it's better than the millions a year that would result from wars.
This is the unspoken validation behind the EU and to some extent the Euro. Without this, the EU machinery would be dissolved tomorrow - it's incredibly expensive, wasteful, incompetent and corrupt*. But it's better than wars.
*And perhaps the same sort of things have been said about the US government. The EU one is probably worse, though, as it is unelected and cannot be influenced by the public in any way.
So to put it simply: Denmark 'telling the EU to [whatever]' is about the same as Rhode Island telling the US government they are seceding, printing their own currency, putting up a border, paying no taxes, issuing RI passports, raising their own army and navy, keeping any US shipping 200 miles off their coast or sinking it, and running their own import controls with the rest of the world.
Ain't gonna happen any day soon
