when a wheel gets bent like that the main thing you see is that the rim is laterally deformed. In fact this cannot happen (esp in a tensioned wheel) without the rim twisting slightly too. The misalignment you see at the rim joint is most likely a result of the net twisting either side of the rim joint.
Now if you straighten the rim in the right way (*) the normal thing is that the twist at the rim joint sorts itself out. However in some cases the joint plastically deforms and retains some amount of mismatch; this will remain until it is corrected.
I have straightened dozens of bent rims and they vary somewhat in how they straighten; some work-harden and reversing bends is actually surprisingly difficult. Others are much easier to straighten. Mavic Module E2 is quite an easy rim to straighten but even so if you have not done it before I would advise that you practice on a scrap rim to develop your technique.
(*) Brandt's book suggests that you back off two turns on all the spokes and then use brute force to get the rim straighter before retensioning the wheel. This is a good way of being able to ride home but it is (IMHO) not the best thing to do if you want to save the rim. The reason is that the when the wheel pringled to start with, the spoke loadings did not greatly affect the mode of plastic deformation (as opposed to elastic deformation) vs a free rim. In fact the main difference would have been that the rim joint would still have had some compressive force across it.
By contrast when straightening a rim it is almost impossible to do this without the spoke tensions interfering (even when they have all been backed off). This means that any straightening (of long rather than short-pitch bends) that you achieve when the wheel is still laced is almost certainly going to be imperfect at least and at worst will do more harm than good.
My suggestion is that you straighten the rim in two stages;
1) with the wheel together but slack, straighten the worst short pitch bends (esp near the rim joint). Then
2) take the wheel apart and straighten the rim properly.
During 2) don't apply any bending loads across the rim joint.
In simple terms the idea is to locate the exact centre of each bend and then to put that region into three-point bending without creating any more damage. To find the bend centres, offer up a rim that is perfectly straight to the bent one and you will see clearly where the bend centres are.
A piece of 4x2 softwood makes a good fulcrum; support the bend beneath one piece and the opposite side of the rim under another. Then (wearing soft-soled shoes) stand on your heels but with your toes 6-8" either side of the bend. Transfer the load from your heels to your toes gradually, so that the bend is pushed back straight.
It will take a few goes before you start pushing the bend back; this is OK; too little is better than too much at this stage. if you think the rim has moved, offer up the gauging rim again and repeat the process. If you are minded to, use a marker pen to keep track of the bend centre positions and directions. I normally don't bother with this any more but it is useful to start with.
A really strong rim will sustain your entire bodyweight at 6", but perhaps not if you bounce slightly at 8". A less strong rim (like an E2) will only take a fraction of your bodyweight at 6" before it moves.
If you get well practised at this you will note that
a) bends have to be balanced either side of the rim; if they are not then a pinned rim joint will always manifest some mismatch.
b) you can alter the width of the support beneath the bend to allow for short or long-pitch bends
c) correcting short-pitch bends accurately is by far the most difficult thing to do; residual long-pitch bends can be allowed for with spoke tension but short pitch ones cannot.
d) if you don't accurately find the centre of a bend and position the fulcrum accurately, the rim might be 'straight' but in fact there will be a residual 'wriggle' in the rim; i.e. you may change a fairly benign long pitch bend into a pair of nasty short-pitch bends that are much more difficult to remove.
As I mentioned upthread it is a good idea to practice on a scrap rim before trying to straighten one that you want to be 'perfect' again. I'd quite fancy my chances of getting a really good result with that rim, but I have had lots of practice.
BTW if the wheel is built with a rim that isn't straight, the wheel will be weak simply because it cannot be both straight and evenly tensioned at the same time. However if the rim is made exactly straight, IME it won't be in any way weaker than it was before.
In practice few such rims are ever *perfect* again and thus don't build into very good wheels which have poor bracing angles or heavy dishing. But they usually build into perfectly durable undished wheels, and if you have a nice front hub like yours (with widely spaced flanges and a good bracing angle) then a good wheel is not that difficult to achieve.
good luck
cheers
