"It is not possible to work with this colleague."
Translation:S touhle kolegyní není možné pracovat.
Yes, your sentence is absolutely fine. The problem here is that we're currently accepting over 2.500 possible versions of this sentence, and that's still not covering all possibilities. :D
But yes, "is not possible" can be "není možné", "je nemožné", "nelze", "nejde" or "nedá se" - the last two are more casual, but dictionaries still list them as standard.
And "spolupracovat" is good and accepted.