Preliminary comment: since you mention a main stack to the right, and a bathroom on the wall behind, best answers would require you to post a diagram of all the DWV in both bathrooms and the main stack. My answers previously and below are somewhat piecemeal without that info, so there may be an oversight. [Conversely, if that left hand vent is a dry vent for a single fixture in the bathroom behind, it might be possible to turn that into a wet vent and use it for drainage from the new lav, which would save you having to reroute the vents as you propose.]
As for rerouting those vents as shown, are they both from fixtures on the floor below? If either one is a fixture on this floor, (WC or shower or tub or whatever, in either this bathroom or the bathroom behind), then you can't have it turn horizontal below the fixture flood rim. [On which basis, since the vent comes up from the floor below, there should be a drain running through the floor system next to or under the wall, so the vent can be taken off plumb or at most 45 degrees from plumb, which still counts as vertical. It's also possible that there is an improper horizontal vent below the floor.]
[On the other hand, if that left hand vent is a dry vent for a single fixture in the bathroom behind, it might be possible to turn that into a wet vent and use it for drainage from the new lav, which would save you having to reroute the vents as you propose. You could even leave the copper double wye as is, assuming you confirm the trap weir rule is complied with despite the wye.]
But if they are both from the floor below, your green rerouting works and keeps you from having to cross the new trap arm over a vent within the wall. [Upon reflection, this doesn't seem too likely, as more typically they would be combined in the story below so that only a single vent runs up between floors.]
As to the drain side of things, you want to put 3 lavs into a single 1-1/2" drain. That is allowed on a horizontal branch, but oddly not allowed on a single floor for a stack. (IPC Table 710.10(2)) So does the 1-1/2" drain basically turn immediately to the right to hit your main stack, or does it proceed downward for at least one story? The latter would make it a stack, which would mean you are not supposed to put in 3 lavs all on the same story, and as an alternative you are supposed to tie into the main stack.
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Assuming you can put 3 lavs into that 1-1/2" copper drain coming up from the floor, since it is 1-1/2" in diameter, you can't use a double fixture fitting, as they all have 2" outlets to my knowledge. A simple arrangement would be 3 separate san-tees, located horizontally and vertically where you want, one for each lav, each with a vent riser to the upper horizontal vent in your proposed rerouting. The fact that two of them would be so close together would complicate combining their drains, but it would be doable. Other arrangements are possible, e.g. one dry vented lav wet venting lav one or two of the lavs, but with that proposed horizontal vent so conveniently located, dry venting each one seem best.
So that's not quite a complete suggestion, particularly on the how the three lav drains would tie together. I'll wait for some more info before commenting further.
Cheers, Wayne