I am very sorry to learn of this situation.
Unfortunately you have a very difficult contractual issue here in that you terminated your lease with your current landlord - they have no obligation to allow you to stay.
What you can do is try to negotiate a deal with them, see if you can offer them a cash deposit, pay an increased rent, or perhaps allow your home to be shown as a model (if that is what they want). I understand none of these are very appealing options, but they are each conditions that you can offer to your current landlord as incentives to get them to change their mind and allow you to stay despite the fact that you have terminated your lease.
With regard to your new landlord. Again, he has no obligation to terminate your lease. However, if you decide to terminate your lease now, he has an obligation to minimize damages.
What this means is that you will be held liable for rent until (1) the end of the lease term; or (2) the landlord finds a new tenant using "good faith efforts" (advertising the unit, not turning down reasonably qualified applicants, and not raising rent). Once the unit is rented, your obligation is over. This means that if they do so before your current deposit is exhausted, you should receive a refund, if your deposit is exhausted, but you have had to pay any rent, the rent obligation will end.
I would not suggest sending a termination letter to your new landlord until you get an agreement with your current landlord to stay - otherwise you are going to be "homeless" for a period (either forced into a holdover/eviction situation, or trying to find a new place to live with your deposit money tied up in the other place, and doing everything in a rush).
Make sure to keep everything in writing (especially any agreements).
Do not rely on Legal Shield or similar products - they can write you a letter, but in my experience they are not terribly helpful. If you need an attorney, speak to a local lawyer, you can find local attorneys using the State and local Bar Association directories, or private directories such as www.AVVO.com; www.FindLaw.com; or www.Martindale.com (I personally find www.AVVO.com to be the most user friendly).