I have been a lecturer and teacher and have the full TEFL post graduate as well as my degree, and have taught from infants to adults and including teaching in a Montessori. Have lived abroad and so experienced all sorts of styles , and in particular have often been asked by bilingual families the best way to help their children learn, in both speaking and writing different languages.
So overall, I do think that reading stories and looking at pictures and nursery rhymes and poetry and songs, are there from very early on within the family, and encouraging bedtime story reading and looking at books together is a really good way to start for any children. We , teaching staff, found that in bilingual families, the best way to grow up with that invaluable skill of having two languages, was for each parent to speak their own language to the child, especially when they are little. So that even if the child asks you something in the other language, if you reply in your native language, they then not only gain the right pronunciation, but also the grammar and structure , which can be very different, with such things as genders of objects or where the verb goes in a sentence. The majority of the children would be a little slower than the single language in learning, but then they are able to assimilate the whole structures, and almost without trying will naturally use the appropriate forms for each one. By the parents or family using their own language, then even if the other parent is a good speaker of a language , the native speaker will make less mistakes .
Then having good books in both language and picture books that each parent can talk about in their own language , also helps . Every country has its own ways and have good and bad points. When I was moving around in Europe, parents who had to move often from country to country, would tend to go for the French Lycee system , because there , whichever country you went to ,the french lycee system was quite rigid and so on a monday in june class 4 would be on page 6 of book 3, so your child would have an easier move, without having those gaps or repeating the same norman history 3 times. But against that I personally think it is very rigid and allowed very little leeway so that the child who was average at a subject would be ok. The child who was advanced would be bored and put off, and the child struggling would be stressed and struggling.
So enjoy being granny and know that when you take them new books and read to them in bed you are helping a lot. I must say that I used to find other benefits for such children, as they were really aware of different ways of life from an early age, could convert their pocket money from one currency to another like the stock exchange and we would have interesting talks about the different things and foods etc that they had. So long as we respect each side and talk about any differences in a positive way , it always worked out well I found.
I will just add a couple of things that I think show how children from quite an early age can figure out how their world works. When I lived in Portugal , my parents came to visit bringing my youngest sister on her first trip abroad at age 4. She looked and listened and then started asking " what is this called and that called in portugese" followed by asking what her name was in portuguese. Then looked round and said " Oh , they just use different words" At her age she was still learning new english vocabulary so saw no difficulty in adding more words. An english friend who had been living there for I think 2 years had 3 girls, The two older children had arrived with english as their main language but soon picked up good portuguese, but the youngest one was only about one when they arrived and portuguese was her first language. Later the father had promotion and went out to, I think, the Bahamas for a while , but knew that they would be moving to Brazil later. The parents decided to keep talking portuguese at home so that they would not lose their good accents etc . The two older children were fine with that , but the youngest, when her father spoke to her in portuguese, looked at him and said in english " they dont speak portuguese here" and after that would respond to any questions only in english and stuck to that. They then moved on to Brazil and she immediately talked in portuguese. They are grown up now but speak several languages which they have learnt from their travels, but we thought that was quite interesting.
I hope I havent gone on too long, but given you some ideas to think about. When they are a little older, and are visiting you or you visit them, then I think that baking is a great thing to do. So there is much measuring and so forth, but you either are telling them how you make your favourite cake, or they are explaining how you make something from a polish recipe and so reading recipes and then enjoying eating the results is a great learning skill, so you might look for a simple recipe book in english for children and take that with you too. I feel personally that children with the opportunity to have two threads to their lives are enriched far more than any slight delay in beginning, and grow up usually with a respect for other people and an open attitude that will help them throughout their lives.