The Players
Hero ($176) is 40ish, has been at the table for an hour, has been somewhat active but not out of line. Has won some, has lost some. No major info for Vs to file away other than one hand described below.

V1 (covers, about $250) is an older gentleman (50s) who is loose but not a full-out fish. Seems willing to call with a wider range than he should but is not a calling station. Previous hand of note between Hero and V2 had Hero raise to $10 in position (with 88) and V1 called from the SB with QJo. Flop came Qxx and V1 check-called. Turn was a blank and V1 check-called again. Hero checked back river and showed losing pair of eights before V1 showed his hand.

V2 (covers, about $300) is a clean cut 20-something. Would not be surprised to find out he is a 2p2er. Like Hero, has been active but within reason and has won some and lost some since Hero has been at the table. I would describe him as a solid, thinking player.

The Action
V1 (seat 8) straddles for $4. V2 in EP (seat 1) raises to $15. Hero (seat 4) re-raises to $40 with KK. V1 thinks for about 20 seconds and calls. V2 pauses for a couple of seconds and calls.

Flop ($123): JJ4
V1 checks. V2 bets $50. Hero...?

You started with less than 100bb and have a 3/4 PSB left. Shove AINEC.

Hero has over psb left to the flop.. Although I'm still never folding

1. they're putting you on AK.
2. Don't most players slowplay trips?

You lose to AJ/JJ/KJ/QJ.
You beat all other pocket pairs, and all club draws.

Shove.
Nh wp.

Pot when it gets to the Hero: $173, Hero has $136 left.
Hero in fact does have 3/4 a PSB left.

If v2 is a potential 2+2er then he should never have a jack or 44. V1 could, but lets not get carried away. Only hand im worried bout from v2 is a sneaky AA or 1 combo of JJ. If I had AA and there was no flush draw I flat this bet all day. Given that your hand is somewhat vulnerable to aces/clubs I think I shove and take my lumps if im beat.

This depends on how risk averse you are. If V2 has been solid like you say, he will likely be strong enough to make a semi-bluff in that situation with a flush draw and over cards. Or, he could have AJ and is protecting his hand. If he thinks you think he is solid, call. If he hasn't seemed to pay you any mind, fold. You'll stand a chance to fight another day...

Thanks for all of the comments. I didn't want to lead the jury too much with my initial post so I left it without comment, but I think that some added thoughts may be of use.

I am looking at an overpair on a paired flop with a flush draw against a Level 1 player and a Level 2 player who has donked the flop for a relatively small price. Let's start with some ranges -

V1 (the level 1 player) cold called a three bet from UTG. We have seen him call a raise light (QJo) from OOP before so his range is somewhat wide but he thought about this call for a while and has not been wildly loose, just a little leaky in his preflop selection. Let's say his range for calling is 22-QQ, AK-AT, and maybe KQ.

V2 (the level 2 player) raised the straddle and then called the three-bet after the cold call by V1. Tricky AA is possible, but doubtful. AK and AQ are in his range, but I doubt he is calling the three bet and call with any weaker Ace when he is OOP to Hero. I think 77-QQ is the heart of his range. Lower pairs are discounted but possible, I guess.

This is Hero's first three bet of the session. I have raised about once an orbit so far but the only raised hand that has made it to the river was 88. V1, being a Level 1 player, doesn't really worry about my range. V2 probably ranges me at AA-JJ, AK, maybe AQ.

The first issue is how worried I should be about someone having a Jack. V2 never would donk small with a jack here. First of all, I think the only hand in his range with a jack is JJ. Second, even if my range is wrong, I can't imagine he would not either slowplay or go for the check-raise if he had a jack. Third, if he has a jack and is worried about a third club coming, he would bet closer to pot. So I conclude V2 does not have a jack.

V1 only has a small number of combinations with a jack (specifically AJ and JJ). I have no postflop info on him so I just have to assume he does not have a jack and proceed accordingly.

How do I proceed accordingly? First of all, I am never folding, both because of my thinking above and SPR.

So, do I shove or flat? And why?

Whether to shove or flat is a functionnof how many out their range has against you and how likely they are to fold to your shove. If V1 will always fold then calling may be best. If he wil never fold TT to a shove then shove. This is actually a good math exercise. You've got ranges. Estimate future action if you shove vs. call and see which one is more +ev. My gut says shove KK but call if it was AA in this spot. The analysis could easily prove this wrong though.