We empathize with the desire to invoke the imahot (the matriarchs) in prayer, both for their own spiritual greatness and for their contributions to the greatness of the avot (forefathers). In practice, we treat much of the language of tefillot as fixed and unalterable. Here too, halacha precludes adding the names of the imahot to the beginning of the shemoneh esrai. In that first beracha, God is described as “God of Avraham, God of Yitzchak, God of Ya’akov.” Shulchan Aruch 113:9 rules that adding to the descriptions of God there is prohibited:
“One should not add to the descriptions of God…specifically in shemoneh esrai, since one should not change the language formula coined by the sages.”
Additionally, Shulchan Aruch 112:1 rules that we cannot add personal supplications to beginning (or end) of shemoneh esrai:
“A person should not ask his needs in the first three [berachot] nor in the last three [berachot].”
Even the propriety of reciting traditional piyyutim (liturgical poems) in the first beracha of shemoneh esrai is debated.
That leaves you with two options for bringing the imahot into your tefilla:
First, you certainly can have the imahot in mind as part of what you mean by invoking the avot, since they were partners.
Second, you can also feel free to add supplications relating to the imahot or invoking their great merit in the 13 middle berachot of shemoneh esrai where we beseech Hashem, before reciting the closing “baruch atah Ha-shem” formula of each.
See more Q&A here.