What I meant, OP, is that you could be made bankrupt or forced to sell your home. And if a judge thought you were doing things vexatiously (so deliberately dragging out a case that had little merit in order for the house to devalue etc) that would go against you in the judgement, as is shown in the bit you quoted above.
The good news, though, if you have no assets, is that you're not likely to be found in contempt of court by refusing (being unable) to pay if costs are awarded against you - so prison is unlikely, as you won't be deliberately not paying what the court has ordered.
If the situation is not that you've been written out entirely (ie disinherited) but you've not been given the third you believe that you are entitled to, unfortunately, you are even less likely to win.
You can, of course, force almost anything to court - virtually everything is arguable, as PP said--but bear in mind that a very hopeless case can be considered to be vexatious also, and you're much more likely to end up having costs go against you as a result.
I remind you of what my colleague said: under a million and lawyers are the only winners.
I really get how distraught you must be feeling. But based on what you've said here, there's a very real chance that you could turn this into a catastrophe even worse than falling out with your sibling and being as let down by your mother in death as much as she let you down whilst she was alive. Of course you are incandescent with rage, on top of everything, but don't let that drag you into cutting off your nose to spite your face, and in doing so, put your children's future at risk.