With regards to your statement:
Looking at GRAMPS and GEDCOM they do not appear to handle the concept of a sequence of children - they seem to rely on knowing their birth dates to sequence them.
I think you are wrong on both counts.
The Gramps Family Editor Children tab allows you to change the order of children in the family. And in fact, Gramps does not use the birth dates to sequence them, but uses the order you select. I believe the default order is the order in which you added the children. If you want to order all the children in your database by birth date, you would use the Third-party BirthOrderTool Addon for Gramps.
GEDCOM keeps track of children using CHIL pointers within a FAM (Family) structure. GEDCOM 5.5.1 states on page 25 that "The preferred order of the CHILdren pointers within a FAMily structure is chronological by birth." That doesn't specifically state that the order of the CHIL pointers should be the order of the children, but most genealogy software developers have followed that standard and will output their order to the GEDCOM CHIL tags and respect the order in GEDCOMs when reading from them. See Tamura Jones' article on GEDCOM Order of Children.
With regards to your case of ordering children by father as well as by each mother when a person has multiple spouses or partners in a polygamous society, here is one thing you can do in your genealogical software program (Gramps or whatever):
Put each person into a family of their own with no spouse/partner. Connect the person with all his/her children and set the children up in the order you want. Birth dates are not required. Not linking to a spouse will prevent the software from trying to group the children by spouse and they will be displayed in the order you specify for each parent. Then all the people will have links to their children and the children will be displayed for each person in the order you want. If you want to record information about the marriage, set up another spouse for each one but don't add children to the marriages - they are just for the partnership information.
I would never recommend building your own SQL database. Genealogy software is special purpose software and using one has very many advantages over unpurposed software, not the least of which is the ability to export and import GEDCOM allowing you to make use of other tools and online family trees.