Child support laws in MD, procedure for seeking reconsideration modification of court order for back child support obligation

Unless there is something really different in Maryland, you cannot file a motion for reconsideration without having another hearing. That being said, if there was an order awarding child support at some point in time prior to last week, that is still an enforceable order so you should be able to collect any back due child support.

If there wasn't an order in place prior to last week, then you most likely will be unable to collect back child support. There wasn't a court order to pay child support so there isn't a legally enforceable obligation to enforce.

Without knowing your circumstances, I am unable to assess the likelihood of getting the modification, but a really important question that you need to ask yourself is this, if you are able to go back into court and obtain the order for back child support, does the other party have the resources to satisfy the judgment if it is entered by the court? You may be spending a lot of energy only to have the realization at the end that, in spite of the court order, if the other party doesn't have it, you are not going to collect it.