I don't know of any DSi quirks that might trouble things (most homebrew tends to be for DS mode, where you can happily do that -- some programs even flipping the ideas of commercial DS games on their head and using the ARM7 as primary brains and ARM9 as workhorse). There is a minimal amount of synchronisation between the two compared to other more developed multicore/dual CPU setups so you will have to handle that as well (you are not quite into full Amdahl's law but will appreciate it).
The devkitpro/devkitarm stuff
https://devkitpro.org/ will contain the GNU assemblers which is where most homebrew devs will land. Some ROM hackers have some others (though frankly most will use the dkp/GNU stuff for things with more than handful of instructions,
https://www.romhacking.net/utilities/635/ if you wanted a start though that version is a bit out of date so go find betas), and there is probably some more buried in the various gigaleak stuff for the commercial DS coding environments (see various how to build pokemon discussions). I don't think I ever saw anybody use the ARM-sdt on the DS; a few GBA homebrew* will.
*speaking of homebrew devkitpro quite notably is very aggressive in removing old versions of it and not all newer versions will compile older code. To that end you may also face issues there is you plan on inlining a bunch of demanding code areas in some existing DS homebrew and just having the rest compile.
http://problemkaputt.de/gbatek.htm#armcpureference is the hardware reference for 99% of people playing on the DS. The no$gba debugger is also good stuff.
For the sake of links though
http://imrannazar.com/ARM-Opcode-Map
http://www.coranac.com/tonc/text/asm.htm is for the GBA but the GBA is similar enough to the DS that I link it anyway.
https://blog.quirk.es/2008/12/things-you-never-wanted-to-know-about.html
ARM themselves will also have listings.