K.S.
Huge hugs to you! Stress stinks when it comes in huge doses like you have.
My 2 cents:
Dogs- they need to be kenneled inside during the day when you can't be there. Take them for walks with the kids everyday rather than just letting them out in the yard. The walks will be good for your stress as well. Schedule a morning walk by yourself early, maybe before your DH leaves for work so that you can have time to yourself just to think and gather your thoughts for the day. Then take an afternoon/evening walk with the kids too.
SIL- these are your DH's sisters, then ask him to step in and talk to them about boundaries. They should know that you would rather have their help than their threats. Ways they can help (and maybe this would teach them that it isn't so easy) could include watching the kids (taking them for an outing) while you get some serious decluttering done. If they can't bring themselves to help, then your DH should severely limit their presence in your house.
Stress/memory- stress causes a depletion of vitamins and the B vitamins are especially critical for memory and brain function. I know money is tight but budget for a B vitamin supplement for you.
Neighbors- Throw a neighborhood potluck dinner on one of these nice summer weekend evenings. A potluck won't cost you anything (especially if you make sure someone will bring plates/cups/utensils as their item. Get to know your neighbors better and let them know you want to be an involved, friendly neighbor so they feel comfortable coming to you directly with problems. Also let your neighbors know that you will be trying some different techniques with your dogs and to let you know if they see (or hear) an improvement.
Get out and away from the kids occasionally. Find a friend who will trade babysitting with you once a month. Go out and do a free activity somewhere with DH or out with a friend for a walk.
Good luck and power to you!