I'm so sorry you and your little guy are struggling with this.
I understand that it would be incredibly frustrating to have a child cry and cry and cry. However, as a childcare provider, it is up to them to provided compassionate care and help the child through that.
I'm not trying to be mean, but I don't think that some home daycare providers have as much experience with as many children, and we all know that children are individuals and all different.... She should be working with you and him on getting through this....
Before you switch, you could try something like this: Get a picture of you and your DH, and put it in a plastic protector, and then work with the childcare provider to find a place where that picture can be posted within easy sight of the child. If you have a favorite t-shirt or nightgown (nothing racy, LOL!), put it there with the picture (your clothes will have your smell on them). When he gets upset, have him go over to the picture, and have the lady keep reaffirming that mommy & daddy are coming back.
I would also give it a couple of weeks before you "give up"---IF you think the daycare provider can get over her frustration and be compassionate. If you don't think she can, then switch. But keep in mind that a lot of changes (one daycare to another in a short period) can be very hard on them. So, I think you might want to just keep him at the current place until the other place opens, so that he doesn't have so many changes.
Definitely talk to the other place & find out how they would handle this scenario (the crying all day), and ask if they have had any kids do that, and how they dealt with it, and moved past it.
Two books you can read with him are "Adam's Daycare" and "Llama Llama Misses Mama" -- read these to him at home and talk about them and how he might feel about going to daycare. He doesn't have the words for his feelings yet, and by starting to give those to him, it might help a little bit. And it will also let him know that you understand how he feels.
You might also try calling the Jobs & Family Services department for your area and seeing if they provide a list of daycares. Action For Children was who helped us, by providing a list of providers for us to contact (they don't make recommendations, but do give info for how to help evaluate the providers). You might google Action For Children and see if they have a service in your area, and/or download their pdf on what to look for in a childcare situation.