We're talking preschool; not kindergarten this year. I wrote the below thinking she was going into kindergarten.
I suggest that most kids that age would've caught up language wise in a year if living in an English Speaking home. Perhaps something else is going on that would mean starting in the younger classroom would benefit her. She has had a very stressful beginning in life. Being behind in language may add to that stress If she's shy and withdrawn. Is she as socially mature as the aaverage 4 yo?
I would have her evaluated by a child psychologist. I would ask how to also have her language evaluated. Does she understand language well but has difficulty responding, for example. I suggest that only a specialist would be able to possibly know how important her placement in a lower grade would be. I suggest you need to consider psychological issues as well as language issues.
I think both you and I may be overthinking this. Smile. Because I adopted a child at age 7 I'm more aware of trauma related issues. I adopted thru the state. Because my new soon to be daughter was having some behavior issues the state did have her evaluated. This reassured me about a successful adoption. Bonding is a major concern. Has anyone talked with you about your children's ability to bond? The report also guided me in knowing how to meet her needs some of which were different because of her early trauma.
If your daughter is adjusting well to your home I would suggest reading about child development. I wonder if the school is talking about language but are also considering social development.
As others have suggested she can start with the 4 year olds and if she has difficulty be moved to the 3 yo room. Do you trust that the staff does have have her best interest at heart? You might want to consider a different school if your sense of what is best in other ways is widely different than yours. What does your gut say.
One reason I thought your question was about kindergarten is I'm unfamiliar with testing for preschool. I know very little about private schools for this age. My thought is that they are a status symbol with a focus on academics. I suggest that because of your daughter's history she needs an emphasis in social learning.
I routinely talked with a child therapist who helped me navigate parenting when my daughter was young. I was also coached by an adoption counselor for over a year after my daughter moved in. You've asked several questions about parenting. I'm glad to see that. I wonder if talking with a counselor/therapist would help you.