Hi Jean,
Your most interesting topic brings to my mind almost immediately, Rembrandt's famous painting "The Polish Rider" (1655) which was originally thought to be an officer of the Lisowski Cossacks. In the painting , prominant under the riders right leg is a clearly heavy sword mounted from the saddle, and on the riders left side can be seen the hilt of what is likely his sabre. While the later research more correctly identifying the rider is most interesting, we are focused on the weaponry he is carrying, and the large sword under his leg appears to be a heavy pallasch.
In European armies, of course in Polish as well, the heavy cavalry seem to have often carried these saddle mounted swords in addition to sabres, but typically they were the estoc (=French; Tuck- English; Koncerz-Polish) which was a long thrusting sword with diamond or triangular cross section for piercing mail or plate armor. Eventually these seem to have given way to the heavy pallasche that were apparantly for fighting dismounted, and as the use of armor diminished.
The only reference I can think of offhand is "Polish Armies 1569-1696" by Richard Brzezinski (Osprey, 1987) which does note these heavy swords, but I cannot recall in what degree. I do recall however an interesting note that shows a Sudanese rider in the late 19th century wearing an Ottoman sabre, and a large kaskara broadsword saddle mounted under his leg, reemphasizing the often romanticized presence of European influence in these regions in anachronistic manner.
This really is an interesting topic, and thought that the use of secondary swords mounted under the saddle may have been last used by the Polish Hussars and possibly into the 18th century. Not having really yet looked further, I am under the impression that most European heavy cavalry of the 18th century were dragoons, and essentially mounted infantry with firearms and with the heavy sword as secondary weapon. The light cavalry that developed had firearms as well, but relied heavily on thier light sabres.
At this point, undoubtedly with exceptions, I would think the type of sword carried was either heavy or light, rather than both.
By the latter 19th century, the cavalry sword had regained larger size, and once again returned to the saddle mount, with firearms at the fore.
Looking forward to your thoughts of course, and those of others!!
All the best,
Jim