You cannot make your mother-in-law pay you child support. The only person who you can demand child support from is the father of the child.
If the child continues on to higher education and lives at home--maybe. If not, you are on your own. Most divorce and child support orders cover this circumstance.
Yes, you should get retroactive pay from the time you filed your unemployment.
In general, parental rights are terminated either preparatory to an adoption, or after a trial in which it is determined that the parent is unfit. In any case, termination of parental rights does not, in itself, terminate child support.
The obligor's spouse can use his/her money, if s/he wishes to do so. However, the spouse cannot be forced to make these payments.