You must do what work for you. Being in tough spot due to finance is not nice place because easy to agree to things you don't want just to get income.
Make sure you document details if you take this family but I do think a trial of three months best idea. If you worried that it might scare them off, please make sure your contacts allow you to give notice not just them.
When things pick up a bit you can decide if you want to keep this family or if you want to look for someone who does not need extra long day. Once you have replacement, you can give notice and say you finding day too long and time notice so they leave just as new person begin.
Don't feel bad about doing this. If parent didn't want your service they would give notice and not feeling bad so you have same right too.