I feel you are making a big deal with onsite. Onsite is not such a big deal afterall.
If you try to resist joining the second project just because of onsite opportunity in some other project it may reflect negatively on you.
I'd suggest go ahead with the second project and try to prove yourself there.
I think if I am getting onsite opportunity then it is because I have proved myself somewhere. Right?
Do you think, We should only prove ourselves without any expectation.
And regarding negative reflection, do you mean that one should not ask for onsite?
I think, I deserve this opportunity and dont want to loose this just because of communication gap among RMG people.