Money is a common thing for couples to argue over, or so I am told. My parents used to.
You say you have tried talking and seeing professionals (who are pretty much trying to get you to do the same) but since you say it hasn't worked I'd suggest the pair of you haven't given it sufficient chance. Airing grievances are one thing, understanding the other person and having a genuine desire to find a solution is the priority.
We only have one side of hate story of course but it seems, on the face of it, that this running out of money hasn't been sufficiently explained. OR maybe it's been and then ignored. There seems to have been no move to overcome the issue. Either by agreeing the financial needs are genuinely different for the pair of you and you need a different split of the family budget, or more likely that one has identified spend that isn't necessary on the finance you both have available and can be cut to balance the books. Why has this analysis not been achieved ? Or if it has why is the solution you guys put into place not working ?
Is there a genuine desire and effort to mend the relationship or is it simply being hoped that discussing the issue without actually coming to an agreement will somehow work it out by itself ?
To answer your question, only you can decide what you do next, but do not take the "split now" option without consideration. It is a big decision and you will have invested a part of your life into the relationship; only opt to go if convinced the relationship has deteriorated and no longer salvageable. It's a big step.
But do not either stay for the sake of the family as it doesn't work to live in misery, and will affect the others, nor plod on (which is much the same thing anyway.
Take further time to think, and if there is still a chance to sort things give the experts and conversations another go. But recall the main thing is to see thee other's point of view (both of you) rather than air the injustices you feel and have a slanging match. Find sensible options, and decide on what you can do.
If all else fails you always have the "get out" option to fall back on.