To answer your first question, no, it doesn't mean the petitioner's mother. The clue is in the ending of reclamante. If the intended meaning was "mother of the petitioner", it would say mamei reclamantei, and reclamantei is a noun.

Instead, reclamante has the ending -e, like an adjective, so this word describes the mother, who IS the applicant/petitioner. And as you say, at the end, your sentence mentions that help is also being given by the maternal grandmother, who is a different person from mamei reclamante, so this is further proof that mamei reclamante does not mean "petitioner's mother". What it means is "the applicant/petitioner (who is the) mother".

Examples:

Mr Justice Keehan:
1. In this matter, I am concerned with one child, 'C', who was born on 2nd December 2014. She is the daughter of the applicant mother, 'A' and the respondent father, 'B'.
https://www.familylawweek.co.uk/site.aspx?i=ed175531

Jurisdiction in divorce, nullity and legal separation is governed by article 3 of the
Regulation (...) A court in England and Wales would have jurisdiction if the petitioning mother were living with the children in the USA and the respondent father were living in this country.
https://www.supremecourt.uk/cases/docs/uksc-2009-0075-judgme...

Beverley Morris, head of Lodders’ Family team, acted for the applicant mother in one of the key reported cases that has shaped this area of law – MT v OT (financial provision: costs)[2008] 2 FLR 1311 , MT V OT [2018] EWHC 868 (Fam).
www.lodders.co.uk/all-expertise/family-law/financial-provis...

See also this relevant RO-ES question where the same phrase came up:
www.proz.com/kudoz/4673318