If you are certain that your grandfather served as a combat engineer and that he was assigned to something with the number 51 in it.I think you can probably be fairly comfortable that he served in the 51st ECBn.The number 51 almost certainly corresponds to a battalion, which I beleive is the highest level of organization for engineers.51 doesn't correspond to a division nor do I beleive it would correspond to a company.Additionally, with the info. you know (Battle of the Bulge, the Bridge at Remagen and Running into Patton's 3rd Army)I think that lends additional evidence to the probability of him serving in the 51st ECBn.
Engineer battalions were either part of a division or were non-divisional.My guess would be that the 51st ECBn was non-divisional, given the fact that I tried doing some searches and could not find a specific attachment to a division.Unfortunately, it is easier to find information at the divisional level.
With respect to doing searches, the best search engine I've been able to find is www.google.com.From their, I would just try any searches you can think of (i.e. the Bn name spelled out, the Bn name abbreviated, specific battles and then include the Bn name or just the word engineer).I have been researching my grandfather's service during WWII for over a year now, and every once in a while, I still find something new.It is indeed a frustrating process.
The other thing you can do is request his military service records from the National Archives (NARA).Unfortunately, that is an extremely slow process (months) and you would not have the info. for your daughters assignment.
Also, given the info. that you do have, she may consider broadening, the scope of her paper just a little to cover the role of the combat engineers during WWII.There is a substantial amount of information on the web on that subject.They certainly had a tough job.