My daughter is the same age and is also very curious about other languages. She's been in a Spanish immersion preschool for three years, and has learned a lot. They absorb so much when they're young. Even if they don't learn to speak the language, just exposing them a bit to other languages and cultures makes them better little people, I think. Just let her lead the way so she doesn't feel pushed into any of it and will continue to enjoy exploring languages. She'll do great with your positive support when her dad is able to teach her a bit.
Here are a few books that have some simple phrases in several languages. My daughter loves all of these:
Yum! Yuck! by Linda Sue Park
Mung Mung by Linda Sue Park
What Is Your Language? by Debra Levanthal (this has a pronunciation guide for all the foreign words in the back - yay!)
Some other authors to check out:
Grace Lin - she has a lot of books about Chinese culture - traditions, food, etc.
Arthur Dorros - his books are written in English, but have Spanish words scattered throughout, and also have lots of detail about Latin American cultures. They also have pronunciation guides for the Spanish words, I think.
George Ancona - he has a lot of books with both English and Spanish text so you can see the languages side by side.
We also frequently just look through the foreign language section at the library and find books that we know, then also check out the English version so we can look at both. I think we had Rainbow Fish in Korean for about a month last year.
My daughter is really interested in Japan right now. She has discovered Hayao Miyazaki's movies (Ponyo, My Neighbor Totoro, Kiki's Delivery Service, and others, but these are her favorites), and has fallen in love with a sweet manga series (like a comic book series) by Kanata Konami called Chi's Sweet Home. We just finished the second book and she is very frustrated that the third is still checked out of our library by someone else! All of these are in English, but have a very Japanese influence.
You may be able to find books about the country where her dad is now - depending on how much you want her to know about what's going on where he is. If he's in the middle east, you may want to look at The Librarian of Basra by Jeannette Winter, or I think Greg Mortenson has a children's book based on his Three Cups of Tea book about Afghanistan.
Keep up the good work. You're doing great!