I would say go armed with everything ..... insurance, EHICs and most importantly a letter signed by the parents to say you are allowed to take the children out of the country. Security is extremely tight these days. As for travel insurance try Endsleigh which specialises in students. Their prices are reasonable too.
They (and you) will need an EHIC card, at least unless we Brexit! It entitles you to free or cheap hospital treatment in EU countries and it is free, you just have to apply. Your insurer will expect you to use it if possible, this enables them to keep premiums down.
If you did need to claim on your insurance, believe me is so much easier if your DGS is on the same policy as you. We have experience of this! Also if you have different policies you can fall between 2 stools if they cover slightly different things.
Insurers will usually add grandkids in for very little extra cost.