I have a PhD and am a junior Assistant professor in tenure track. I had a chance to do a post-doc at an ivy league school, but accepted the tenure offer from a more teaching and less research school. I want to advance my career, and I believe part of the reason I couldn't get into a research school was my PhD university which is well known but not in US. I am thinking of doing a part time post-doc or getting an MSc in an ivy league school to help me advance my career (Machine learning/Data science field). Publication in my field take a lot of time and by the time that I have made an established publication stream I will not be as young and ambitious as I am now.
How awkward is it if an assistant prof does part time post-doc on summers (when not in contract) or even during the year?