Ted, I've followed your story from the beginning, and despite the obvious hurdles you've had to overcome this year, I am pleased for you that at this point you now have confirmation of your polish daughter's paternity, and that your wife is now fully aware of the situation.
The sticking point to me, seems to be the issue of telling your English daughter about her half-sibling. I want to make it clear that my personal viewpoint is that you should be telling your English daughter as soon as possible. My reasoning is as follows:
Your polish daughter is already aware of her half sibling. You say that your wife does not believe in the possibility of her searching for your English daughter on social media in the next 6 or so years (I would say that regardless of social media rules and parenting ideals, that age 11 could likely be the age that she would be starting to use such platforms), and I wonder if this is because your wife and yourself are of an older generation who really minimise the idea of the social media prevalence in today's youth. Regardless of whether your English daughter currently uses social media or not, the facility to attempt contact will continue to be there, and I believe it would be far more distressing for your English daughter to find out in such a shocking way.
You have absolutely no idea as to how your English daughter will react to the news. Yes, it is possible that she will be furious with you for having an affair/ side with her mother/ refuse contact with you. However, your daughter is not an emotional teenager. She is a grown woman with 2 children of her own. Her maternal instinct to her own children, really should allow her some insight into your reasons for wanting to continue your relationship with your polish daughter. She knows the overwhelming love for a child, she knows the feelings of duty and responsibility that all parents should hold, and should eventually come to terms with the fact that regardless of your polish daughter's conception, you should be and continue to be involved as any proper up- standing father should be. It may take time for her to deal with her emotions after receiving such news, but you are her father/ have been there for her throughout her life, and you will not stop being her father just because of the decision you took 6 years ago. Her love for you and her lifetime of history with you, should not be wiped away, purely because of this. If my father had done this, I would be angry/ go through stages of upset and anger, but would come out the other side in a stronger place of knowing I was fully in charge of the facts, and could make my own informed decisions about attempting to create a relationship with my new half-sibling if I chose to do so.
Currently, your English daughter is unaware of the issue, but has obviously noticed your distancing yourself from her, and a level of secrecy and odd atmosphere between her Mum and Dad. Right now, she could be imagining all sorts of scenarios, with either you or your wife scared to tell her of a terminal diagnosis, or severe money worries, or anything. The turmoil that you could be unwittingly creating in your English daughter is completely unfair and avoidable. Family secrets such as these do immense damage, and should not be kept for everyone's sake- honesty is always the best policy, regardless of the short-term upset they will undoubtedly cause.
On the other hand, as you do not know how your daughter will react to the news, you do not know where her anger and frustration will be pointed towards. If I was to find out on my father's death bed that he had fathered another child, after I had processed the hurt and anger at his actions, if I then discovered that despite his longing to tell me, my own mother had refused his requests, I would be absolutely furious at my mother for creating a lifetime of deception, and for denying me the possibility of forging any relationship with that sibling. You and your wife have a duty towards your English daughter to furnish her with the truth right now. The possibility that your daughter could be more angry towards your wife's continued deception until your death/ will-reading, is a very real possibility, and I am sure you do not want to irrevocably damage their relationship.
On the subject of age-gaps, the younger your polish daughter is when she starts communicating with your English daughter, the better. Children are more adaptable, more resilient, more open and loving, the younger they are when they start to form relationships with adult family members. Your English daughter would have far more chance at creating a loving sibling bond with her sister at this age, than she would when they are both adults. Your daughter even has the experience of understanding her own children of a similar age- their likes/ dislikes/ fads & behaviours- she would be more in-tune with this half-sibling now, then at any other point in the future.
In my personal life, I have a DSS who will be 20 this year, and who lives 5 hours away from us. He has a wonderful, loving relationship with his younger half siblings (17, 15, 7, and 1) who live with us, which has been built and maintained over the years via 3 or 4 yearly trips either way/ regular Skype or WhatsApp or phone calls/ social media with the older ones/ inclusion in family events/ random letters and pictures and jokes sent through the post either way. 3 months can go by between real-life visits, and our 7 year old still runs to him and plays with him, as though they were never apart. Despite the distance, sibling relationships can flourish if all the adults involved put the effort in.
And on another point in my personal life, 15 years ago when I met and began a relationship with my DP, he had my 2 DSDs with his ex-partner, then aged 5 months and 2 years of age. Plus he also had my DSS, then aged 4 years of age, who lived at the other end of the country. My DP and the 2 mother's of his 3 children had, had their children very young in their teenage years, and for one immature reason or another, my DP had gone along with a request from the mother of his 2 daughter's, to not tell them of their half-sibling's existence. Absolute idiocy and stupidity I felt, which within a year of our relationship became a deal-breaker for me, as I felt I would be unable to continue a relationship with a man who I felt was not putting the emotional needs and future lives of all his children first. This decision of my DP could have been a red flag, but we were all very young and immature back then.
The fall-out of defying his ex-partner's request to keep his son a secret until his daughters were teenagers was immense- withheld contact/ damaged civil relationship etc, but it was absolutely the right thing to do. Within a few years, amicable relationships resumed, and now 15 years on, the relationship that all 3 of my DSC enjoy with each other as near adults is solid/ unwavering/ supportive/ loving and will hopefully last a lifetime. I dread to think of how damaged their relationships with each other or indeed their parents would have been, had the ridiculous secret been maintained throughout their childhoods.
This is just my perspective- one of many that you have read on your post, but I truly believe that once you have told your english daughter, once the dust has settled and your daughter forgives you and moves on, once your wife has chosen to stay or leave; the polish mother will know that your intentions and long-term hopes for a relationship with your polish daughter are more clear and obvious, and will open up the contact arrangements again. Her request for a sibling relationship has not been fulfilled, but if you take that step, she will know you are serious about her daughter being in your life long-term.
The limbo that you are living in, is unhealthy and damaging to your own health, let alone your polish daughter's emotional and mental well-being at growing up knowing she is a secret, let alone your English's daughter's right to a choice in her life and her possible worries about what on earth is bothering her parents, let alone your wife's mental well-being with holding this secret inside herself as well. It is indeed unfortunate that you intially agreed to your wife's request to never tell your English daughter, but realistically this request cannot be adhered to. Swallow your fear and calmly inform your wife that you will be telling your daughter as it is the only option available for everyone's sake.
Take the step to a better life- emotionally, mentally, and honestly, for the sakes of all your family members.
Tell your daughter.