Hello and thanks for your question.
The rule on international/cross border family disputes concenring children is that they must be dealt with by the court in the country where the child normally lives.
As your 6 year old has a British passport, I am guessing that she lives in the UK, and therefore you can apply to the family court here.
What you need to do as a first step and as an emergency measure, is to apply to court for a prohibited steps order, prohibting the removal of your daughter from the UK, until the court has had time to consder the situation fully.
As it's an emergency application, you should be able to get an ex-parte (ie without notice to your wife) hearing within days. That order then needs to be served on your wife, and on the police who will under the Port Alert scheme circulate it it to airports etc, so that your wife would be stopped at customs if she tries to take your daughter out of the country. You also need to send a copy to the passport authority to prevent your wife applying for another passport for your daughter by saying that the original is lost. Also, you can send a copy to the Czech Embassy if you think that she will rey to get your daughter a Czech passport.
For your application to court, you will need to justify why the order must be made as an emeregency eg you have seen one-way tickets in your wife and daughter's names, or overheard telehone conversations saying when she is going to take your daughter etc.
The form you need is C100 - here:-
To argue for a hearing at very short notice, you need form C2 - here:-
Simultaneously on the same form C100, you need to apply for a child arrangements order for the court to order that your daughter should live with you in the UK. For that, you need to show why that would best for your daugher eg that she is settled in school, has lots of friends, speaks English better than Czech. You will also need to show how you would look after her if her mother went back to Slovakia, and how you would reduce the child' s distress on being parted from her mother, plus what steps you woudl take to maintain the child's relationshio with her mother eg via regular tel calls, emails, skype etc.
The mother would be arguingall of the above but in reverse ie why it would be better for her daughter to live with her in Slovakia. The court will have to decide where the child's welfare would best be served.
I strongly advise you to get some face-to-face legal advice. Here's where to find a specialist family law solicitor:
I can also highly recommend the charity Reunite International who specialise in advising people in just your situation. They also have a specialised mediation service to help people reach agreement rather than go to court.
I hope this helps and I wish you the best of luck.
Thanks and best wishes...