We are in a similar situation as well. We have not asked the friends yet, but plan to.
As far as timing, I'd wait about 3-4 months, things should've settled down at that point. It is a BIG responsibility, so its very possible they'll say no. Just remember that it is probably NOT about you, but too much for them to handle, if they do say no. I'd approach it by talking about how you're doing your will and really struggling to decide who would be the best one to take care of your kids. Just be open and honest about the concerns with asking your family, and let them know that you really appreciate them as friends and respect their family values. Would they consider filling this need for you?
As far as family having hurt feelings, that will likely happen. In our case we would trust both of our parents to take care of our kids, as far as raising them as we'd want them to be raised. However it would be a huge financial burden for my in laws, and my parents are way too over committed already, I fear our kids would fall through the cracks. Our siblings do not share the same values, and two of them are single women, the married couple also struggles with drug addiction, so definitely NOT them. Anyway. I would not sit down and talk to my family about why they are not being chosen. Most likely this situation will not happen, so why bring up the drama. If your friends do agree to do this, then you would need to draw up some guidelines on visitation with your family, any limitations you might have or how often etc... Its super important for the kids to stay connected to their family as well, at least on the level that they are now, if not a bit more for their emotional needs.
If you do feel you'd like to talk to your family about why not, then really sit down and figure out why you don't want them. Will it be too much of a financial burden, or do their values not meet up with yours. No stable home life... Whatever it is. Focus on that being the reason, not that you don't like them. Try to pick something noninflammatory, if possible, even if it isn't your #1 reason. Like I wouldn't mention to my brother's family that I'm not picking them because of their struggles with drug addiction, I'd focus on it being too much of a financial burden for them (which is also a legitimate concern). Explain that you are not trying to keep your child from them, but put them into a home that is as similar to the one you set up for them as possible. Explain how the visitation would occur with the other family or any other thing you think would be helpful.
Anyway, I understand your need to get it done yesterday. I feel the same and I have a 3.5 year old and a 1 year old. I know in a situation like this social workers try to keep kids and families together, so your family members would need to step up and fill the need if something happened to you both before you had a chance to talk to your friends.