Since I can see it in her eyes that she wants to communicate but is not able to and I can see it bothering her a lot.
One of the Amerind languages was reputed to be so hard that native children weren't fluently competent until about age 8. It is possible that if a child needs to speak 4 languages, it will take longer before they reach competency in all of them (or the first).
I did baby sign with my toddler until he started talking. Wrapping your tongue around the words is hard. As soon as he started talking, he stopped signing. (He's learning English primarily and a little Tagalog and Russian)
It's all about exposure. The languages where you don't get enough exposure will degrade to receptive ability alone. Personally I think that still counts as resource because if someone needs to upgrade their skill from receptive to fluent in adulthood, it will be easier than if they knew none of the language at all.
Also, this is more than 2 languages-- if you can come up with "system" for when to speak each language, that helps. For example, language X outside of the house, language Y when reading and watching TV, language Z in mixed company. I don't think the mixing is a problem, in the Philippines, language mixing is an obligatory part of the language. I think the issue is that if you don't have a system for switching, you can easily end up in the same language all the time.
The ability to acquire the next language just by hearing it degrades continually from age 0 to 18 or so. The old rule of thumb was age 4, now the answer is more complicated-- kids can move to a new language community and be accent free up to about age 6 or 12.
The practical upper limit for learning languages by growing up surrounded by them is about 6 for communities where the entire community is multilingual. ref: http://www.amazon.com/Babel-No-More-Extraordinary-Language/dp/1451628269
What could possibly go wrong? This seems to be the underlying question in these sort of questions (and the answers)
People who for social and cultural reasons are palpably afraid of the implications of speaking more than one language around kids-- they don't have a leg to stand on. So far, I've only read about children who have unstable lives where they keep moving one one monolingual community to another and dropping the old language and not quite learning the next-- those kids can end up fluent in no particular language. To really confuse children (my parents won't stop talking about my toddler being confused), you need colossal poverty, chaos and so on.
Also, make sure you kids understand you best language or you understand fluently their best language. There are cases of parents who end up unable to speak to their children in any language because they tried to hard to make sure their kids spoke the community language alone and the parent never had time to learn the community language.
My opinion is that it is a parent's job to teach their kids the languages necessary to fit in with the world they will grow up in. If you kid will be working the international bureaucracies, international sales and so on like it sounds like you do, they you should feel obliged to teach them as many languages as they might need to know. To pull off 4 languages, or even three, you may need to put some thought into fitting enough exposure into the daily schedule to give the child enough input to gain fluency.