I'm sure I'll be back here with more questions, as my wife hasn't heard of TaxAct (I presume we start here:
https://www.taxact.com/ !) and I haven't.
Regarding the joint accounts, it is difficult to keep the finances completely separate. We use that for things like holiday money and whatnot; it's a tricky line to walk because on the one hand, keeping the finances separate might be smart for tax purposes, but for visa purposes we like them to be mixed up a bit! I think we're probably best trying to keep a nominal amount in the accounts, such that they don't exceed, e.g. £4000 in total at any point, so we're below the reporting threshold. Is this smart to try to balance the two competing requirements?
Goodness, so many complicated things to figure out - I wish I had more experience with tax stuff so I didn't feel so lost with it all. We just want to make sure that we're doing the right thing by both the US and the UK governments in terms of tax and visa things! Thanks so much for everyone's help.