There is plenty of literature to support the understanding that families are children's first teacher but I am unable to find actual research on this topic.
I have been looking for relevant research, but it does not seem to be very identifiable. I hope there is something here, but maybe not mentioning the phrase 'first teacher'.
These might be of some relevance:
Gest, S. D., Freeman, N. R., Domitrovich, C. E., & Welsh, J. A. (2004). Shared book reading and children’s language comprehension skills: the moderating role of parental discipline practices. Early Childhood Research Quarterly, 19(2), 319-336.
Schaedel, B., Hertz-Lazarowitz, R., & Azaiza, F. (2007). Mothers as educators: The empowerment of rural Muslim women in Israel and their role in advancing the literacy development of their children. International Journal about Parents in Education, 1(0), 272-282.
Kakia, L., Popov, H. N., & Arani, A. M. (2016). A study of relationships between parents’ and teachers’ demographic factors and their judgments about children’s activities and school readiness in primary schools of Tehran. International Journal of Comparative Education and Development, 18(2), 100-119.
Rowe, K. J. (1991).The influence of reading activity at home on students' attitudes towards reading, classroom attentiveness and reading achievement: An application of structural equation modelling. British Journal of Educational Psychology, 61(1), 19-35.
I'm not sure whether this is relevant for your question:
McClelland, M. M., & Morrison, F. J. (2003). The emergence of learning-related social skills in preschool children. Early Childhood Research Quarterly, 18(2), 206-224.
Connor, C. M., Son, S. H., Hindman, A. H., & Morrison, F. J. (2005). Teacher qualifications, classroom practices, family characteristics, and preschool experience: Complex effects on first graders' vocabulary and early reading outcomes. Journal of School Psychology, 43(4), 343-375.
Tazi, Z. (2015). Arte Juntos/Art Together: Promoting School Readiness among Latino Children through Parent Engagement and Social Inclusion in a Suburban Museum. Museum & Society, 13(2), 158-171.
Have you looked at research carried out in Africa where there are orphans (due to AIDS) who have not had the same parenting as those brought up in the family situation?
Very best wishes for your literature review,
Mary
Article Teacher qualifications, classroom practices, family characte...
Article The emergence of learning-related social skills in preschool children
Article The influence of reading activity at home on students' attit...
Article Beginning Literacy with Language: Young Children Learning at...
Data Gest, Freeman2004
Article Israeli Educators in a Multi-Cultural Community: Jewish and ...
Article Arte Juntos/Art Together: Promoting School Readiness among L...
Article A study of relationships between parents’ and teachers’ demo...
Our projects with low SES Jewish mothers and with Arab mothers indicate (see our publications) that when mothers are instructed how to read a book and engage with their child at home in literacy development (homework, games) it has a positive impact on their childcare's achievement scores.