Dobrý den,
státní příslušnost není otázkou, která nějak souvisí s výkonem rodičovské odpovědnosti, je závislá na právu státu, jak stanoví pravidla pro nabytí státní příslušnosti. Jak právo ČR, tak SR umožňuje dvojí státní občanství a je naprosto běžné, že dítě Čecha s Slováka má obě státní občanství a ani souhlas či nesouhlas jednoho z rodičů s věcí nijak nesouvisí. Nicméně fakt, že dítě bude mít také slovenské občanství nezakládá právo matky se s dítětem odstěhovat na Slovensko. To je již zásadní záležitostí, na které se rodiče musí domluvit, tedy druhý rodič musí souhlasit.
Hezký den

Dear madam,

in spite of the fact that a father and a mother live in different countries, Czech law admits to the children the child support. The amount of the child support depends on many factors provided by law, there is no exact set amount in the law. However, Ministry of justice prepared the chart of estimated amounts of child support per month, which can be used by You and the father as approximate quidance for setting the amount of child support.

Age of the child --> percentage range from father´s net income
0 – 5 years --> 11-15%
6 – 9 years --> 13-17%
10 – 14 years --> 15-19%
15 – 17 years--> 16-22%
18 and older --> 19-25%

However, this chart is only informative and approximate, every case is strictly individual and there are many principles which have to be and are considered by Czech courts in cases that the parents are not capable of agreement.

The principles regarding child support are defined in the Civil Code (section 910 and subsequent).

To determine the extent of maintenance and support, justified needs of the obligee and his property situation, as
well as his abilities, potential and property situation of the obligor are decisive.
In evaluating the abilities, potential and property situation of the obligor, it should also be considered whether the
obligor has not given up, without a good cause, a more favourable employment or gainful activity, or property benefit, or whether
he is not taking unreasonable property risks. Account should also be taken of the fact that the obligor personally cares for the
obligee, and of the extent he does so; account shall also be taken of the care for the family household, where appropriate.

Where there are several obligors in the same position to the obligee, the scope of the duty to maintain and support
each of them is proportional to the relation between their property situation, abilities and potential and the property situation,
abilities and potential of the others.
In principle, the standard of living of a child is to be identical to the standard of living of his parents. This principle
is superior to the principle of justified needs of the child.

If a court decides on a parent’s duty to maintain and support a child or an ancestor’s duty to maintain and support a
minor child who has not yet acquired full legal capacity, and if permitted by the property situation of the person obliged to
provide maintenance and support, justified needs of the child may be considered to also include the generation of savings,
unless excluded by the circumstances of a special case; the maintenance and support provided passes into the ownership of
the child. Administration of the amounts so provided is governed by the general rules on child’s assets and liabilities.

Here you can find the English version of the Civil Code: http://obcanskyzakonik.justice.cz/images/pdf/Civil-Code.pdf

Best regards