New parent need help picking interchangeable lens camera vs DSLR

I am a amateur photographer and planning to get a new camera.

I almost bought Nikon d5100 DSLR and came across mirror less cameras and its buying guide on this site.

Now I am confused btw the two types. I have listed my top needs below. Can you please help me decide.

• I have an infant and planning to use my new camera for photos and videos mainly inside our house for my little princess.

• I am also planning to take photography class and get into next level of photography

• I love traveling and I usually take my tripod and Sony dsc3 with me all the time.

• my hand shakes a bit whenever I take photos and am looking for appropriate camera which will nullify it.

Thanks a lot for your help.