PICUS is defined in Part FCL as
"a co-pilot performing, under the supervision of the pilot-in-command, the duties and functions of a pilot-in-command." Nearly all references in
AMC and GM to Part FCL refer to PICUS in the context of a co-pilot of a multi pilot aeroplane. For instance :
"PICUS flight time: provided that the method of supervision is acceptable to the competent authority, a co-pilot may log as PIC flight time flown as PICUS when all the duties and functions of PIC on that flight were carried out in such a way that the intervention of the PIC in the interest of safety was not required."
There is a body of opinion that says that PICUS therefore only refers to multi-pilot aircraft but there is another (slightly smaller) body that point to a single clause in the AMC that says
"the applicant for or the holder of a pilot licence may log as PIC time all solo flight time, flight time as SPIC and flight time under supervision provided that such SPIC time and flight time under supervision are countersigned by the instructor" to imply that 'flight time under supervision' countersigned by an FI is PICUS that can be logged as PIC.
It would seem to me that, if your children held a valid licence on a single-pilot aircraft and signed for it as PIC, then whether you are an 'observer' or not is irrelevant.
Nothing more definitive that I am aware of, but FIs may have a clearer view.
Not sure why you say that, if you get a frozen ATPL without a job, you have to start from scratch again to get a full ATPL. Can you explain?