Since you'll be working for the govt, you have to declare and get permission from the ethics board if you're going to work elsewhere - they want to make sure govt people arent using their status in the govt to make money unethically outside. It should be fine if it's 10 hrs/week though. Your schedule sounds pretty brutal, and actual hours worked in lab will depend on the lab. It could be possible especially if you have a understanding mentor but you have to decide how much of a life you want to have and how much free time. I do ec's outside of NIH that probably take up more than 10hrs/week, but I'm lucky my schedule for ec's and work is flexible.