Learn Spanish (Latin America): Ella pidió el helado de todos modos.

De todos modos translates to "anyway" or "in any case." It shows that despite some unmentioned obstacle, the action still happened. Yes, you can absolutely use de todas formas here; they are completely interchangeable concessive markers in this context.

Why does pedir become pidió instead of pedió?

Pedir (to ask for or to order) is an -ir verb that changes its stem from e to i. In the past tense (preterite), these -ir verbs undergo that stem change only in the third-person forms, like he, she, or they. That is why the e changes to i to make pidió for ella.

Why use pidió for "ordered" rather than a word like ordenó?

While ordenar exists and is sometimes used for food in parts of Latin America under English influence, pedir is universally understood and is the most common, natural way to talk about ordering food or drinks in Spanish.

Could I move de todos modos to a different part of the sentence?

Yes, just like "anyway" in English, this phrase is very flexible. You could put it at the very beginning of the sentence by saying De todos modos, ella pidió el helado. Placing it at the beginning or the end is entirely up to your preference and the flow of the conversation.