I applaud your ambition, but i can’t imagine how this would be work. You’re employed full time, you’re in grad school full time, and you’re a new father—- how would you actually have any time to do an internship? How much time you could actually give? How would you be able to concentrate enough to learn the concepts and apply them to actually be a net contributor to the company after a certain amount of time? As someone who who has hired many interns and seen some work out and others not, I don’t see that you’re setup for success- and the type of team that would bring you on in this situation likely wouldn’t be one you would want to learn from.

I don’t know all of your situation, but if I we’re looking at your profile, having an internship as a software engineer would make think you’re more de-risked as a hire than having a grad degree.