I did a little more research and it appears that she will get 50% of the equity in the home that you jointly own. Check out the Partition Act for details. However, there is no equity in the home, so there's nothing to split. She can argue that there is 150K (as a gift) equity in the home, but you can argue this with your supporting documentation. If you provide proof of the debt towards the house, then a judge will subtract that debt from the value of the home. She can argue it, but what evidence does she have that would indicate the 150K was a gift?
Fair enough about you needing to show that you gained at her expense. Actually, the onus is on the party arguing unjust enrichment, to show the deprivation on her part and the subsequent gain on your part.
Thankfully, I've never been involved in SS and it seems complicated. Sure, every spouse has an obligation to provide support for himself or herself and for the other spouse, in accordance with need, to the extent that he or she is capable of doing so; however, other stuff is taken into consideration:
(a) the division of function in their relationship;
(b) the express or tacit agreement of the spouses or common-law partners that one will maintain the other;
(c) the terms of a marriage contract or separation agreement between the spouses or common-law partners;
(d) custodial arrangements made with respect to the children of the relationship;
(e) the obligations of each spouse or common-law partner towards any children;
(f) the physical or mental disability of either spouse or common-law partner;
(g) the inability of a spouse or common-law partner to obtain gainful employment;
(h) the contribution of a spouse or common-law partner to the education or career potential of the other;
(i) the reasonable needs of the spouse or common-law partner with a right to maintenance;
(j) the reasonable needs of the spouse or common-law partner obliged to pay maintenance;
(k) the separate property of each spouse or common-law partner;
(l) the ability to pay of the spouse or common-law partner who is obliged to pay maintenance having regard to that spouse's or common-law partner's obligation to pay child maintenance in accordance with the Guidelines; and
(m) the ability of the spouse or common-law partner with the right to maintenance to contribute to his own maintenance.
I found a recent case that covers a lot of your situation. They were common law, jointly owned home, had two kids and mom hardly worked. They had a cohab agreement, but the judge detailed his decision in terms of the cohab and without.
CanLII - 2011 NSSC 34 (CanLII)
You're already paying her $1,500/month, but you have the kids and she's not paying any CS. If she's not working, then she needs to step up to the plate, get a job and start financially contributing to her kids. If I were you, I would be pressing that issue; you're not the only one who has financial obligations from the partnership.