Tamarind is decidedly acidic. Although the dilution ratio is an important factor, I'd avoid reactive aluminum. As Abbie points out, anodized cookware doesn't present a problem. On the other hand, cast iron is also reactive.

Brown in batches however you see fit, just don't crowd the pan(s) during that step. That rule doesn't apply to the braise itself so cram things in as necessary. I wouldn't worry about aluminum reactivity unless your braising liquid is acidic. If you're braising in an oven, bring everything up to temperature (a bare simmer) over a burner beforehand to minimize any timing issues.

I don't think I would use the aluminum pot unless it's non-reactive, like Calphalon. Can you fit both dutch oven in your oven at once? I guess you can't cram all 15 lbs into one pot - if you CAN, I would brown it in batches, fill the pot, and increase the cook time. Is this a low and slow / juicy gravy recipe or are you looking for crispy as in Carnitas??