Its not free for all schools back.
The nurseries and primary schools will be opening first. Most have continued to run at reduced capacity for children of key workers and the vulnerable with low staff ratios and social distancing, cleaning etc and this is being opened to more people than key workers
As far as I was aware there is no obligation to send your child but I will check this (am in private school also, keyworker but have kept my kids off as DH was home)
'Secondary education' 6th to 10th classes are still home until 10th May at least with distance learning as before.
Greenlynx - I work in this area. While the virus is still spreading in the community in DK its been controlled at a rate that means that patients who need to be in hospital, and need ventilation are able to obtain it. ICUs here are nowhere near capacity (approx 1000 ventilated beds are available across the country) and are able to cope with corona work as well as the usual sick patients that require intensive care. Not all ICUs are open to corona either, a lot of work has been going on to cohort isolate corona patients in certain places and hospitals which allows concentration of both infection risk but also some development of expertise (given its a new variant of virus we are still working out what it can do and how best to provide organ support). No testing for antibodies but there is an increased program of testing being rolled out.
This website www.sst.dk/da/corona/tal-og-overvaagning
has the latest figures (it should be reasonably easy to translate a few words to understand the graphs) and is updated about 1-2pm every day. As of 2 pm today there were 408 patients in hospital with Corona with about 106 in ICU, and 90 of those being ventilated, though its not spread evenly across the country. I am not sure of the exact number of cases self isolating at home on top of this but the health service is coping at present
Also most of the other non elective functions of the health service are still running, eg if you need chemo or a cancer op you are still getting it without a delay, though elective operations have been paused.
It has also been discussed that this phased reopening of the schools is not a given and the plan can be reassessed and lockdown resumed if required.