Need help with measure

This measure is created using a detached Date dimension - as can be seen from this data model:

Doing that makes it possible to calculate the correct distinct count, using this DAX:

Antal verserende sager = 

VAR MinDato = MIN('FilterDato (Verserende sager)'[DatoFilterKey])

RETURN

CALCULATE(
    DISTINCTCOUNT(FactArvesager[ArvesagsKey]),
    FactArvesager[Forventet afsluttet Dato] >= MinDato && 
    FactArvesager[Bostarts Dato] < MinDato &&
    (FactArvesager[Realiseretarv Dato] = BLANK() || FactArvesager[Realiseretarv Dato] >= MinDato),
    USERELATIONSHIP(FactArvesager[Forventet afsluttet Dato],DimDato[DatoKey])
)

The VAR MinDato gives the  minimum date in my date filter:

But the datamodel is not that userfriendly, and I would like to use the date from my Date dimension (DimDato) instead of the detached date dimension. 

The problem is that when I use the Date dimension it gives me the wrong result. If I use this measure:

Antal verserende sager test = 

VAR MinDato = MIN(DimDato[DatoKey])

RETURN

CALCULATE(
    DISTINCTCOUNT(FactArvesager[ArvesagsKey]),
    FactArvesager[Forventet afsluttet Dato] >= MinDato && 
    FactArvesager[Bostarts Dato] < MinDato &&
    (FactArvesager[Realiseretarv Dato] = BLANK() || FactArvesager[Realiseretarv Dato] >= MinDato),
    USERELATIONSHIP(FactArvesager[Forventet afsluttet Dato],DimDato[DatoKey])
)

Were I use the Date Dimension (DimDato) instead of the detached date dimension, I get 4 records more:

The minimum date is 1. april 2022:

The green row is correct since it is before the minimum date and the filter in the measure works, but the 4 red rows is not correct as can be seen - since all 4 records is after 1. april 2022.

To me it looks as if the variable MinDato (= minimum date from the datefilter) is calcualted differently than I would expect.

So therefor I need to have a detached date dimension. Can You tell me how to get the date correct?

Any help is really appreciated 🙂