Hi Tia,
Almost all editing software today will do "picture in picture". All you're doing is resizing one of the images and placing it into a corner if the master image.
Are you running a Mac or a PC? Knowing that will give me a better idea of what software to recommend. If you are looking for the ultimate in flexibility using top notch products, I'd point you to the Adobe "Creative Cloud". For $20.00 per month you have access to ALL of Adobe's industry standard products like
Premiere their editing program. Here's the link to the site:
https://creative.adobe.com/
Good luck,
Michael