I can't tell you what the lender will do if you offer a deed in lieu. A short sale will eliminate your obligation for the mortgage, but most short sales fail to materialize, because, just like the deed in lieu, the lender must accept, and most of the time, it doesn't.
If you all a foreclosure, you will be hit with both a deficiency judgment and a tax bill from the IRS for "cancellaion of debt" income. You can avoid the tax effect if that home is your principal residence at the time of foreclosure, but that won't avoid the deficiency itself -- only bankruptcy or a deed in lieu/short sale will accomplish that.
If you intend to let the house go to foreclosure, then having a tenant may bring you income, but not enough to overcome all of the other downsides. Financially, you come out better to move the tenants out, move yoursel in, let the lender forclose and then file for bankruptcy. The fact that your husband's home has no equity means that you can keep it -- otherwise, you would have a pretty impossible situation.
Re the car, you could sell it, and put $5,000 into an IRA, assuming that you make regular annual contributions to an IRA. Otherwise, the court may find another fraudulent transfer. Then you could buy a cheap car and between the car and the IRA you would be able to save ~$8,000 of the car value. The remaining $7,000 woud be lost to your creditors.
One other thing. If your rental has a large 2nd, that mortgage can be wiped out in a Chapter 13 filing, which would leave you with only the 1st. Same goes for your husband's home. This is called a "cramdown," but it only works for Chapte 13 and it only operates on junior liens/mortgages.