Amy has developed (by one analysis) two auxiliary verbs! She's apparently taken them from German adverbs.
She uses "gerne" (roughly, "gladly") to mean "would like to/want to" and "lieber" ("rather") to mean "would rather". For example, "Ich gerne das haben" = "I would like to have that" (while pointing at a toy in a catalogue, for example); "Ich lieber Ucke essen" = "I would rather eat cucumber [than what I have on my board now]". Properly, that would be "Ich möchte gerne das haben" and "Ich möchte lieber Gurke essen", with the auxiliary "möchten"(? - not sure what the infinitive is), "to want, to would like to".
Note that her "auxiliary verb" is in the proper position for one (second position in the sentence) and the main verb, in infinitive, is at the end.
She also uses "gerne" to refer to others, e.g. "Mama gerne auch das essen?" = "Does Mummy want to eat this, too?" or "Mama gerne auch das essen." = "Mummy would like to eat this, too" or even "Mummy, you want to eat this, too." (What an assertion!)
Another thing she says is "Darf das haben?" or "Kann Buch lesen?" for "May I have this?" or "Can I read (this/a) book?".
I wondered whether she doesn't know to include the subject, but she does say "ich" in sentences such as "Ich gerne das haben", so perhaps she's merely having trouble with the subject-verb inversion used in sentences such as this (in English and German), which would explain why the subject gets left out only in questions (V1 order) but not statements (V2 order).
Also, she seems to have abstracted the word "not" in English, which is pretty good, I think, given that I typically use contractions when speaking to her. (I'm guessing that German is helping her here, where the word remains unreduced "nicht".)
For example, she'll say "I not go potty" or "I not have ladybird pillow".
I'm not sure how to encourage her to say that -- I'm glad that she's using the English word "not", but if I want to repeat her sentence, I'll typically do so not in her words but in mine, which will involve, more often than not, a contraction such as "won't", "don't", "haven't", "aren't", etc.
In a vaguely-related note, it seems that Stella (frequently, if not always) calls Amy's potty "der Potty" now rather than "das Töpfchen". This amuses me :)
I'm not sure whether she adopted that word from me or from Amy (I'm guessing the latter).
It reminds me of when I was small, when there were certain words in our family which we borrowed from English into German; the ones that come to mind right now are "der Shed" and "das Study", referring to our bicycle/tool shed and my father's study/den, respectively. (Hence, sentences such as "Daddy ist im Study" -- phonetically, roughly /dEdi Is Im stEdi/.)