I don't know that much, just that before the Poor Clares of the Immaculate were what they are now, they were previously Urbanist Poor Clares (in Italy).
Britannica says:
QUOTE
The [Poor Clare] rule was revised a number of times until, in 1263/64, Pope Urban IV issued a rule permitting common ownership of property, greater self-governance for the order, and other concessions. The monasteries adopting this rule came to be called the Urbanist Poor Clares, or officially the Order of St. Clare (O.S.C.), whereas those communities who continued to observe the stricter Rule of St. Clare (as revised in 1253) became known as the Primitives, or Poor Clares (P.C.). Early in the 15th century St. Colette of Corbie (1381–1447), in France, sought to reform the order, restoring the primitive observance in 17 monasteries during her lifetime and reasserting the strict principle of poverty; her followers came to be called the Colettine Poor Clares, or Poor Clares of St. Colette (P.C.C.), and today are located mostly in France. The Capuchin Sisters, originating in Naples in 1538, and the Alcantarines, of 1631, are also Poor Clares of the strict observance.
From
http://www.ofmconv.org/English/st.clare.htm:QUOTE
In the year 1263 the original rule underwent a final modification at the hands of Urban IV. On 18 October of that year the sovereign pontiff issued the rule which is in the most general observance among the Poor Clares and which has given the name "Urbanist" to a large division of the order. It is noteworthy that in Urban's Rule the new community received for the first time the official title of "Order of St. Clare". In a few particulars the new regulations were less severe than in the rule of 1247. For instance, the abbess was empowered to dispense with the obligation of silence during certain hours of the day at her good pleasure. The sections of the rule are arranged in a new order and are divided into twenty-six chapters. For the most part the very words of the previous rule are employed. One important change must be noted. Innocent IV had left the Second Order in charge of the general and provincial of the Friars Minor. Urban IV withdrew from these officials practically all their authority over the Second Order and bestowed it on the cardinal protector.