Sounds like a good plan, but maybe a little fast. Maybe drag it out an extra day or two. Yes, I would put them back under the lights. Doesn't make much sense to put them out for 2 hrs and then in the dark for 22hrs. There's almost 15 hours of daylight now anyway. IMO don't pinch the flowers, but others might feel different about that.

Here's a different opinion. I take mine outside in a shady area and don't bring them back in unless the temp gets below 40F. Each day you can increase the sun exposure little by little. I would also take off the blooms until they are in the ground.
Just my 2 cents - John A

Unless we have very cold temps forecasted (like John, around 40 degrees F) once my tomatoes go outside, they stay there. I do cover them with a double layer of shade cloth, for the first two days if we have full sun, then reduce it to one and by the end of a week or 10 days, they are getting full sun.

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Betsy

I like to keep mine outside, too. I just move them from sun to a shady location. Even in the shady location they will get some of that great natural light, not to mention the fresh air and a little breeze. You probably know that part of the hardening off process is to get them accustomed to breezes/winds.

Agree that once they go out they do best if left out. Back and forth, in and out can be stressful for them as they keep having to re-adjust.

But that means only when day and night temps are ok and you need to make a somewhat wind protected and shaded area for them outside not just set them out on an open deck in the sun.

Dave