The purpose of this study is to determine if the addition of infusions of a type of immune cell called a "natural killer", or NK cell to the sarcoma chemotherapy regimen GEM/DOX (gemcitabine and docetaxel) can improve outcomes in people with childhood sarcomas that have relapsed or not responded to prior therapies.

The goals of this study are:

* To determine the safety and efficacy of the addition of adoptive transfer of universal donor, TGF imprinted (TGFi), expanded NK cells to the pediatric sarcoma salvage chemotherapeutic regimen gemcitabine/docetaxel (GEM/DOX) for treatment of relapsed and refractory pediatric sarcomas To determine the 6-month progression free survival achieved with this treatment in patients within cohorts of relapsed or refractory osteosarcoma, Ewing sarcoma, rhabdomyosarcoma and non-rhabdomyosarcoma soft tissue sarcoma.
* To identify toxicities related to treatment with GEM/DOX + TGFi expanded NK cells

Participants will receive study drugs that include chemotherapy and NK cells in cycles; each cycle is 21 days long and you can receive up to 8 cycles.

* Gemcitabine (GEM): via IV on Days 1 and 8
* Docetaxel (DOX): via IV on Day 8
* Prophylactic dexamethasone: Day 7-9 to prevent fluid retention and hypersensitivity reaction
* Peg-filgrastim (PEG-GCSF) or biosimilar: Day 9 to help your white blood cell recover and allow more chemotherapy to be given
* TGFi NK cells: via IV on Day 12