Unfortunately, there is no ready-made variable that identifies these groups. There are, however, a number of different family interrelationship variables (both Census defined and IPUMS defined) that may be of use for you. The Census defined family variable is FTYPE and the IPUMS defined family variable is FAMUNIT. These two definitions of families are not necessarily the same. I suggest reading into each definition (see previous links) and using the definition that works best for your work.
Identifying married/single/cohabiting families with and without children could be done using Census derived variables or IPUMS derived variables. Census variables include: ASPOUSE and PECOHAB and can identify self-reported family type. FAMREL can be used to count the number of children (if any) within the Census defined family. IPUMS derived variables include: SPLOC to identify if a person’s spouse lived in the same household based on probabilistic programming, this can be used with MARST to identify marital status, and NCHILD identifies the number of children (if any).
I hope this helps.