Hi C.,
Consider yourself extremely lucky to have a trustworthy child care provider! They are difficult to find. I would not make it an issue, and I would just pay for that week. After just losing her father, I am sure she has other concerns she is dealing with right now and doesn't need any added stress. Plus, if your child was at a Kindercare, etc, you would be paying for every week of the year...holidays, vacation, summer...whether your child attends that week or not. That is just their way to hold your child's spot in the daycare, so you still have a better deal with your friend if you pay for that week.
Check out the site www.freecycle.org. It is an excellent source of baby items, etc. For my first daughter, we didn't pay for anything except diapers, and co-pays for doctor visits, literally. Everything else was gifted, handed down, or acquired from freecycle. Why spend tons of money on fancy stuff, when everything is outgrown so quickly. And at such a young age, they don't realize that their clothes were already worn by their older cousins.
Believe me, I totally understand watching the budget especially with one on the way (I have two little ones myself), but jeopardizing access to quality child care is not worth it!
Good luck and congrats,
L.