Concerns on Interesting Facts About Homeschooling

First of all, before anyone says “why do you have to re-home her’”, it’s a complicated situation between us not being able to give her the attention she deserves anymore, and the fact that she is desires attention from me or my husband only and well, to be honest with 2 other kids and a newborn on the way we won’t have the time for her. We want what is best for her and what is best for her is a new loving home. If you’re going to slam us for that, please don’t answer. I’m 9 months pregnant and this is hard enough as it is.

Anyhow, on to my question.
We have her in a temporary home (a friend of mine offered) until we can adopt her out. Problem being that it’s been nearly 2 months and no one has adopted her. Three people have been interested, but change their minds at the last minute.

We’ve attempted to contact some local (within driving distance) dog rescue groups. None of them have the space for her and want us to keep her in our home until they can place her. We just can’t do that at this point, which is why my friend is keeping her for now.

We are running out of options quickly. My friend can’t keep her forever and we can’t take her back into our home. What else is a reasonable option that doesn’t involve putting her in to a city shelter that may euthanize her’ We do NOT want that. But we also can’t/won’t take her back into our home after knowing we won’t have the time or energy to give her the attention she needs.

Please, helpful answers only. This isn’t exactly the greatest situation, I know, but originally we didn’t even plan to keep the dog when she was given to us (my sister bought the dog, then dumped it on us the day before I had my daughter about 4 years ago). We meant to find her a home long before this, but had the same issue (no one would take her). But at the time my husband made more money and I had more time to give to both my kids and the dog. Now my husband makes less money and we’re adding another newborn to the family and I will be homeschooling my kids in the fall. *sigh* It’s a sucky situation all around.
I just realized how long winded this was! Sorry.

The question is:
What else is a reasonable option that doesn’t involve putting her in to a city shelter that may euthanize her’ What can we do to find her a new loving home in a timely manner’
She’s a lab/husky. But if you don’t live in my area, how can you re-home her’ (just asking)