Hello,
my name is Liliana, i have over ten years of experience as a designer, and what i like most is illustrate, that's why i like this project.
Please, visit my Freelancer portfolio https://www.freelancer.com/u/webpolis.html
to see some of the illustrations and cartoons i made, in order to evaluate my work.
I can send you more family illustrations samples, if you want to.
I use Illustrator for this kind of projects, i can deliver you the images as vector format, and also saved as any other format you may need, like JPG, or transparent PNG, for example.
I found this project really enjoyable and interesting, and i would like to create an original, simple and fun family scene illustration with the background that you described, that match with the style of the home page mockup that you attached.
I hope we can work together, please, contact me if you have any questions, or if you want to see some more of my work.
Best regards.
Lili.