You have it backwards. SSI has income limits and does figure a step parent's contribution to the household for eligibility purposes, if the child lives in the same household. SSDI does not have an income threshold. There are limits on how much income the recipient can make and still receive benefits, but no one else's income is considered in determining who gets benefits.
I am not sure why you wouldn't be paying child support, especially if the mother does not work, but that is between you. If the child is disabled and currently receiving SSI and will not be living with her mother, and a stepparent with income over the threshold to qualify for benefits, SSI will be terminated. The mother absolutely could file for a modification and there is a 99.9% chance it would be granted as courts believe that the biological/legal parents are the ones responsible for the support of a child.