Learn Farsi: ما می‌خواهیم با بچه‌ها شنا کنیم.

In Farsi, when you express a desire like wanting to do something, the second verb needs to be in the present subjunctive form. Since می‌خواهیم (we want) sets up this desire, the main action شنا کردن (to swim) drops the indicative میـ prefix and takes the subjunctive form شنا کنیم.

Doesn't the subjunctive usually start with the prefix بـ? Why doesn't شنا کنیم have it?

Good catch! Usually, the present subjunctive adds the prefix بـ to the verb stem (like بروم, I go). However, شنا کردن is a compound verb made of شنا (swimming) and کردن (to do). For compound verbs using کردن, we usually just use the subjunctive stem کنـ without adding بـ.

Do both verbs need to match the subject "we" (ما)?

Yes, exactly. In English we say "We want to swim", where "swim" is an infinitive. But in Farsi, both verbs must be conjugated to match the subject. So we literally say "We want that we swim", using the "we" ending ـیم on both می‌خواهیم and کنیم.

Why is با بچه‌ها (with the children) placed in the middle of the sentence?

Farsi verbs like to go at the end of the clause. In sentences with a modal verb like "want", the first verb (می‌خواهیم) usually comes right after the subject, and the second verb () goes at the very end. Extra details, like who you are with, get sandwiched between them.