Disclaimer: I am not a lawyer. As for dual taxation, I have some practical experience with Germany/Italy and Germany/Lithuania, but not specifically with Czechia/Germany.
I take it that you are a non-EU citizen but staying in the EU on a blue card, which allows the (non-EU citizen) holder to live and work in the entire EU, except for Denmark and Ireland.
As such, you would be allowed to live and work in Germany as well as in Czechia. Hence in terms of residence and work permit, Prague would not be an issue. Norway might be a different story – while part of the Schengen area, it is not covered by the blue card.
Taxation might be an issue, and a somewhat less standardized one – there is no such thing as a common taxation area; rather, it is down to agreements between the individual states involved. What you want to look at is an agreement on dual taxation between the Czech Republic and the Federal Republic of Germany. These tend to look at factors such as the number of days spent in one state or the other, which state the entity paying the salary is located in, and where your main residence (“Lebensmittelpunkt” in German) lies.
If your salary is paid in Czechia (i.e. by a Czech company), that would be an argument for taxation in Czechia.
If your husband and children live in Germany, then Germany would likely be your “Lebensmittelpunkt”, a factor in favor of taxation in Germany.
Three days per week in Prague add up to a maximum of 156 days, which is less than half of the year. If you consider vacation days, it might come out at even less, but if you were to decide to stay in Prague Wednesday to Wednesday, including the weekend in between, and/or spend your vacation in Czechia, you might end up spending more than half of the year there. Spending the majority of the year in one particular state tends to be an argument for paying your taxes there.
In short: As far as work and residence permits go, Prague/Czechia is likely the easier option. As for taxation, things are more complicated. Maybe your new employer has the expertise to help you on this if they offer contracts to people working in other EU states nearly half of the time. Other than that, you can either choose to study the dual taxation agreement between Czechia and Germany, or get professional advice.
