Law / Maintenance & Rights: Polish mother & child in Poland, Irish father in the UK [57]

Hi All,
I would like to have some info about how does it work out in Poland for the my case as follow:
I was living along with my kids and their mother in Poland for 4 years over.when i went on holidays to visit my parents abroad, the mother brought a man home just the day before i came back to Poland (2013 June), my daughter told me there was a sweaty uncle who was sleeping on my side of bed ,,and she does not like him because he was breathing strongly and sweat was dripping from him on the her ,

I said to myself forgiveness is a great tool But the same year( 2013 August ) I was home at night sitting watching some news and the mother who invited a friend who on a trip from UK to Poland at our home, I saw with my own eyes in front of me on the balcony , the mother was having sex with him on the balcony she already had her night dress( they went on the balcony couple of times to smoke), I was surprised and , the man did have his 2 kids with him, i told him to leave at the earliest in the morning ,as it was around 01:00 in the morning when they were having sex on the balcony and wet weather and he was on alcohol

I tried even that to bring us back , tried very hard but could stop thinking what kind of mother she is ,I move out by October 2013.

I could not stop thinking about that.How could a woman does not have respect for herself or for the kids.When I look at her i just can't believe it

Now she put the case to Court in Poland looking for alimony ( 2000 Pln for 2 kids, I am sending her around 200 euro as she is working in a good position well paid ) which i think is too much. I did send the APPEAL to court even my lawyer was in court to represent on the hearing day me ,as I am on training for new job.I am not working at the moment( my lawyer is in a town over 400 km to the town where the hearing is).

And she did file a case for Parental rights, and the first hearing gonna be in October 2015,No when i asked her I would like to visit the kids where they spend some times with me during my 2-3 days when will be on visit there she told me , she has to take a day off for that, It looks like a to supervised

What are the rights of a father in this case Please?
And I do not understand why supervise when the court did not rule out any hearing yet about restriction or so.?
Should I look for a lawyer in the town where the case is ? and should i ask the court about her behaviour supervising me or what so ever she is having her mind?

Thanks in advance for your replies