Hi febes,
How lovely that she enjoys ballet so much.
I had two children with language delay, one sorted himself out in his third year (though I now realise that I had worked out quite a few techniques to help him that I now see in language books), the other required intensive help from me and I could have not worked full time whilst providing the level of help he needed. The chances are that if her language is such that you call it "very delayed" at 3.5, then you and your DH are going to be getting even more busy than you no doubt already are helping her! This is no bad thing - it will probably be much more fun for your DH to get a real handle on how to help her than to just get wound up....
You've put your finger on the true problem already - her communication problems are preventing her from doing some of the things that 3-year-olds need to be doing. So even if the biological language-development-thing (it doesn't matter what we call it) just sorts itself out (as it did eventually in both my kids - and perhaps in your DH too by any chance? ) she isn't having all the beginning-to-socialise experiences that you want her to be having at this age and that you observe the other kids having ....
In terms of health professionals, first of all, eliminate hearing problems (if only because health professionals won't consider anything else until glue ear is eliminated). Please don't take no for an answer.
Then, in terms of you and your DH using the best techniques you can, the simplest, best-written and most guaranteed non-scary, jargon-free book you can buy is "It Takes To to Talk". This is published by a charity called Hanen. They sell it on their website at hanen.org for a lot of money, but people on this forum usually buy it from a publisher called Winslow for about £32. Someone will link for you if you can't find it. I recommend this from the library of books in my head because you and your DH can both use it and you can show it to anyone - including the Kindy staff - without triggering arguments/defensiveness/panic. If you are going back to work full time, she is going to need help from both of you and the staff, working as a team and starting right now. This book will show you and DH appropriate techniques to bring on her language. It will help you become confident - she will have the advantages that the child of a speech therapist would have.
You mentioned that she doesn't listen. Consider also buying the poorly-named but very good DVD set "Teach me to listen and obey" from the www.teachmetotalk.com site. I recommend this because there are many many materials on helping children talk (almost too many) but astonishingly few materials that attempt systematically to show you how to help them listen.
Meanwhile, keep in mind that she may have some sensory problems and she may have more problems understanding and processing language than she does speaking it. She may also find it easier to make sense of the world if she has lots and lots of unchanging visual markers in her life like photographs of the places she goes to, a calendar by her bed that you use to tick off the days and mark special events, perhaps her own camera, etc,etc.
Think about whether you want to take her to a speech and language therapist once you have the hearing test results. They will assess her. If you know her communication is behind, you are likely to end up with a report saying exactly that. If that will galvanise you and DH further, so much the better - if it might depress/paralyse either of you, then think carefuly about how to stay in control of the process: you two are the star players in her team, and you need to stay on top form. But speech therpists are the ones who are really really good at working out if this is a problem with hearing, listening, processing what she hears, formulating a response, moving her mouth muscles to make the response, understanding the social rules behind to-and-fro conversations, or a combination of these. if it wasn't any of them, she'd be communicating as her peers do.
Come back if you want to talk more but no one can take in everything at once. As for worrying - just get too busy to worry. You'll soon have mustered all your teaching skills to work out clever ballet-themed games to help her communicate better. good luck.