No, the two 90s on the lav drain aren't a problem, they would both need to be LT90.
The geometry is a little tricky, though, I'm trying to think of how to do it elegantly. As you drew it, you'd need a fitting that connects horizontally to the tub drain, horizontally to the lav drain, but perpendicular to the tub drain, and the common outlet is vertical. That would be a san-tee with sanitary side inlet and the top entry blocked, a bit unusual.
You could consider the following, which would let you keep the tub trap and trap arm at 1-1/2", allowing you a bit more vertical leeway, although you may still have to adjust your existing tub trap height:
The lav drain comes through the subfloor and hits a LT90 to run to the the left in your picture (towards the tub). It runs past the shower drain by at least 12". Then it hits a horizontal LT90 to go through the joist (check the height limits on the hole), where it hits a horizontal combo to join the tub trap arm. That shortens the tub trap arm to under 72". The combo outlet needs to be 2" (so it could be a 2x2x1-1/2" combo, with a 2x1-1/2" bushing in the straight entry for the tub). Then the 2" runs back to the line of the shower drain, where it turns down to join it.
As to that last detail, here's a slightly more elegant way to join the 2" tub/lav drain between the joists with the 2" shower drain below the joists, assuming you have enough clearance in the joist bay. First the tub/lav drain hits a 45 pointed downward, then it hits the side entry of a combo on the shower drain, where the combo is rolled 45 degrees off upright, so that the 45 outlet and combo inlet line up.
Then if you do that how far you run the lav drain towards the tub is limited on the low end by the need to leave room for the horizontal combo, 45, and rolled upright combo all in a row. There's also a limit to how high up in the joist bay the lav drain can start, assuming you are installing the LT90 from below. If you install a 1-1/2" LT90 with the hub tight to the subfloor, the centerline of the outlet will be a little under 3-1/2" from the top of the joist. If you are able to open up the subfloor sufficiently for access, you could install the 1-1/2" LT90 higher, with its hub partially or fully above the bottom of the subfloor.
Cheers, Wayne