With it being summer, utilize the help of your other children! They may still be quite young and I am not sure of thier temperment but children/siblings need to be given responsibilties to help care for the other members of the family and household duties! Especially in a home with a singe parent. Your children are all probably feeling the stress of you losing a job, of moving, of a mother who is feeling over whelmed and alone (and unless you are super mom it would be impossible not to be feeling this way!) Even a 4 year old can be trusted to sit and sing a song or tell a story to your infant while you pack in the same room. Your 12 year old can hold the baby while you pack or can pack simple items like clothes, toys, linens and non breakable dishes while you supervise and hold the baby.
I have 3 sons who all were very snuggly babies. We didn't believe in allowing them to cry for more than a few minutes, as we felt that when baby cries it is for always for a reason. And unlike many pople who say let them cry or you will spoil them, I don't believe you can spoil an infant!
What I did do when I put them down and they would immediatly arch thier backs and start to cry, is tell them what I was doing, "Mommy is going to put you down now, you are just fine, I am right here" ect. I was always talking and laughing with them, allowed them to see me, waved to them and then I did everything I could think of to distract them before I picked them up, squeezed a squeaky toy, put in a loud movie, sung a song!
Remember that as difficult as this move may be right now, you are moving towards a support system. Children will be more affected by how well you handle the stress you are under than the actual trials you are facing.
I have a sign that says, "When life gets to be more than you can stand, KNEEL! I don't know how religious you are but Pray! For your children and for yourself! Good luck and this too will pass!