I am in the need for some answers relating to New quee

Unfortunatly, I have been busy with work and family this spring, and
my 2 hives have not recieved the attention needed.  So, bees being
bees, they both swarmed on 4/12  (19 Days ago) about 3 weeks ago, and
didnt hang around for me to catch them.    According to the books, the
new queens should emerge 2-4 Days after the swarm, First Flight in
another 3 days mated in another 3 and Laying 5 Days Later  (Total of
15 days - if my numbers are right).  I waited until yesterday to look
for eggs and need some answers to what I found.

Another interesting (to me at least) bit of information.  I had marked
queens (visually seen during inspections) in my hives last spring -
lots of bees and lots of honey - only one swarm which was caught and
subsequently recombined with the hive it came from -  When I checked
the hives last fall, I visually spotted unmarked queens in both hives
(supercedure).  Brood pattern was excellent, so I stuck with them and
considered it a Requeened hive.  I thought of requeening this spring,
but build up and pattern was good, they were less than 7 month old
queens, so I followed the "Aint broke dont fix it" rule...  no Sugar
Syrup or Pollen was fed to either hive, and they were still going like
gangbusters - resulting in the swarms.

Hive #1 was devoid of any sign of a queen.  No Eggs, No Larvae, No
Capped Brood.  (At least 21 days since the last egg was laid)
My Hive 1 concerns are that there is no Viable Queen within the hive -
or have I not waited long enough to see her evidence.  Lost on her
flights, Ate by a bird, etc.

Hive #2 had No Larvae or Capped Brood, but I did see eggs in a random
pattern on 2-3 frames (the eggs were well placed in the cells -
standing up in the bottom of the cell, and no evidence of multiple
eggs in a cell).  So - it has been at least 21 days since the old
queen laid eggs, and the new queen has not been laying eggs for more
than 3 Days.
Hive #2 Concerns are that the queen was not well mated (sporadic
pattern).

Has enough time elapsed since the swarms that they should have been
laying and at least seen lots of eggs, and maybe some small larvae.
Should I give them a few more days to become established (then requeen
in the fall) - or find the queens in both hives kill them and requeen
now?

Thanks
Rod Billett
Lexington, SC