Just to cap it all there's a honeysuckle growing through the rose and Bishop Weed all through the bed. You have really got your work cut out.

Haha. Yeah, it's definitely a bit of a mess! But understanding what's there is at least a good start! Thank you, @floral and @Embothrium! I'll try to add a close up of the vine growing up the trees. There's a ton of virginia creeper growing in the area too. Would that climb up the trees? I wouldn't rule out poison ivy, but haven't seen any yet. I'll keep my fingers crossed we don't have that on top of everything else!

oh, I see- you're saying it's bishop weed rather than Virginia creeper. That would be a bummer- when we saw all that we thought "well at least it's native". How can I tell the difference between the two?

The creeper is a woody climber - such as the one on the tree - and the weed is a carpet forming perennial plant. One whose top disappears during the winter, comes back again in spring.

thank you!

Bishop weed has pinnately compound leaves, Virginia creeper has palmately compound leaves. BW can't climb and isn't woody. Once you know the difference you'll never confuse them. They're not very similar.

BW is a thing you'll curse and hate forever, don't you dare take a bag of earth from there to use anywhere else in the garden. That's pretty much the only thing you can't kill in this lifetime in that area. And that black earth you just added prerhaps for a vegetable garden, is unprotected from it. Maybe you can still dig in a wall of at least 20 cm deep between the weed and your planting bed.

For the vine, don't worry. You can always cut it, just wait until it's in leaf to decide if you keep it or not. Give your garden a summer without intervening - it will tell you what grows where, where is the right place for planting stuff. That hedge might protect you from scorching sun or from your neighbour's sight. Next winter is time enough to plot and plan and modify to your heart's desire.

Thanks everyone for the great info and advice! So quick update: here are some close ups of what's climbing up a number of the trees. It looks to be two different vines- a thin one with some leaves that look a bit like grape leaves and a thick one that isn't blooming...at least not yet. Any ideas on what it is or what to do about it?