There were never, to my knowledge, any orders of knighthood specifically dedicated to women alone. There were women in some of the military orders, like the Knights Hospitaller, but they were usually addressed as 'sister' and were not awarded knightly status.

One military order, the Order of the Blessed Virgin Mary, does appear to have had female members who were referred to as 'militissa', female knights. However there is no evidence that they participated in combat or the order's military duties. It is likely that this title was a form of confraternity, an associate membership where laymen or women could pay to support an order and in turn benefit from the order's services and reputation.

The Order of the Hachet, one of the orders referred to in the source you quote below, likely did not exist. It is cited in Ashmole's The Institution, Laws, and Ceremony of the Most Noble Order of the Garter (1672), but this is a very unreliable source for chivalric orders. Ashmole often confused chivalric orders with military-religious ones (such as the Order of the Dragon). He also presented some proposed orders as being actually founded, when in reality they never made it off the page (e.g. the Order of the Passion).

For the Order of the Hachet Ashmole specifically cites Josef Micheli Marquez, probably referring to his Tesoro Militar de Cavalleria of 1642. This work is also highly unreliable. For example, in his book Marquez discusses the Brician Order, or Knights of St Bridgit of Sweden, citing Marcus Antonius Vianus Polonus and Brother Antonius Boisius as his sources. It seems that neither of these men existed. There is also no evidence of a Brician Order until Marquez's book in 1642. It is likely that Marquez misunderstood the discussion of a secular knighthood ceremony in Bridgit's writings as that of a proposal for a military order. The case was likely the same with the Order of the Hachet. Antiquarians elaborated a brief account of women knights into the creation of an order.

If the Order of the Hachet did exist, it probably did so as a one off, with these women created knights in 1149 and no further members inducted. A later misreading or elaboration of this evidence then resulted in antiquarians turning a one-off creation of knighthood into an 'order'. The Wikipedia article for this supposed order further highlights the unreliability of this area. Each of its three sources is a website. The Spanish version references later antiquarian works that cite Marquez as their source. There do not appear to have been any academic works published on this order, suggesting it never existed.

Sources:

Elias Ashmole, The Institution, Laws, and Ceremony of the Most Noble Order of the Garter (1672).

Myra Bom, Women in the Military Orders of the Crusades (2012).

Hans Cnattingius, ‘The Order of the Knights of St. Bridget’, Annales Academiae Regiae Scientiarum Upsaliensis, Vol. 11 (1967).

José Micheli y Márquez, Tesoro Militar de Cavallaria (Madrid, 1642).

Can you cite examples? When and where?