I've seen this question in various places, and it only makes sense since F:NV is essentially an expansion of FO3, there really no engine changes in between games, so theoretically NV mods should work with FO3 and vice versa. The Weapon Animation Replacers mod for NV is probably my favorite mod for the game because it fixes the one real thing that consistently broke the immersion for me, the horrendous character animations. As it turns out, you can use this mod in FO3, i did it last night and it's working flawlessly even with RH Ironsights installed. Maybe I'm a noob and you guys have already figured this out, but for those of you who don't here's a tutorial, which I'll try to keep as brief as possible.
Firstly, make sure you have no mods that change the weapon animations, that includes RH Ironsights. If you only have RH ironsights installed, leave it, as you have to install that mod first.
What you're going to do next is download both The Commando and The Professional Weapon Animation Replacers off of the NV Nexus Page found here: http://www.nexusmods.com/newvegas/mods/38527/?
Next, you're going to go into your Fallout 3 directory(Steam version). I'm running Windows 8 but it should be a similar process on previous versions of Windows, which would be My PC/©:/Program Files (x86)/Steam/SteamApps/common/Fallout 3/Data/meshes/characters. Now in the "characters" folder, there are two folders called _1stperson and _male, these folders contain the first person and third person character animations respectively.
Now, install the RH ironsights mod using your preferred method, whether it be NMM or FOMM.
Next step is to open up both The Commando and The Professional using an archiver, I use Winrar but I believe you can use anything such as Winzip, 7zip etc.
Keep this in mind, in both mod packs you'll have options called Core Animations and Optional Stances. Do NOT use any of the First Person core animations otherwise you'll interfere with RH_Ironsights and mess up nearly all of the first person animations and render most iron sights unusable. What you're going to do is go into Core Animations (in both packs), Third Person Animations, and copy and paste all of the files in those folders into the _male folder in your Fallout 3 directory. What these are going to do are change the way your character aims, attacks, and moves with all of the guns in third person.
Now, go into the Optional Stances folder of both mod packs, Third Person. The Commando should have optional third person idle stances for rifles and assault rifles, with two options for each, look at the .jpg included in the folder to see which one you like best, then choose Relaxed, Heroic, or Default. Those three choices all have options 1 and 2 within them and don't really change the stances too much, I generally choose Relaxed. Go into whichever option you want and copy all of the files in that folder into the _male folder in your Fallout 3 directory.
Now do the same for The Professional. There are four options here, pistols only. Personally I usually go with Relaxed, option 3. You're going to do the same as you did here for The Commando. Choose your preferred option and copy the files into the _male folder in your Fallout 3 directory.
We're almost done, now all we need to do is change the first person stance and only the stance. Once again do NOT transfer any First Person Core Animations.
For both packs you're going to go into Optional Stances, First Person, and just like before choose the stance you want, go into the option you chose, and there should be one animation file within copy that into the _1stperson folder of your Fallout 3 directory.
And that's it! If everything was done correctly, you should successfully have the NV Weapon Animation Replacers working flawlessly in Fallout 3 along with RH_Ironsights. Enjoy!