My husbands ex wife, is on ssi, he pays child support, and he has never missed a payment, it comes directly out of pay roll, daughter is not coming around because of being mad at her dad and I, can his ex file taxes and claim daughter, out of spite, and keep him from not fileing

Claiming a child can get complicated for matters other than the basic deduction, but in general the parent who has the child the most claims the child.
And he still owes support regardless of whether she visits or not.

Since his ex is the custodial parent she can claim the child as her dependent even though he pays child support, unless either (a) there is a specific stipulation in the divorce decree giving your husband the right to claim the child as his dependent, or (b) the ex voluntarily signs a form (which he must attach to his return) relinquishing her right to claim the child as her dependent. You can see the details of how this works on pages 10 and 11 of IRS pub 501:
http://www.irs.gov/pub/irs-pdf/p501.pdf

I don't see how this is keeping your husband from filing his taxes - he just can't claim the child as his dependent.

If the husband is on SSI and that is his ONLY income, he probablyh has NO legal requirement to file.

If he cannot claim the child, he will get no credit of any type, so why file?

If the husband is on SSI and that is his ONLY income, he probablyh has NO legal requirement to file.

From what the OP wrote I think it's the ex-wife who is on SSI, not the OP's husband. Note that child support is paid directly out of the husband's pay check.

Yes, you are correct. Then her filing is truly out of spite, because SSI is not normally taxable income.

Many people call it SSI when they mean SSDI. It's possible to work part time under a threshold and still collect SSDI, get a refund, get EIC and child tax credits and so on.

Okay, if there is earned income, then filing and claiming the child makes sense tax-wise.

It does not change the fact that she should NOT be claiming the child.