OP I am in your situation but reversed. I am trying to force the sale of the property I jointly own with my ex, which he is currently living i n and refuses to sell. We have a joint mortgage, joint owners, not married. We also have young children. He's a total financial screw up and is trying to drag me down with him (in case you're wondering why I need off the mortgage with him) 
I have had legal advice and we are a fair way through the process. He is living there and has our children with him alternate weeks (we have 50:50 residency). The advice I've had may be helpful to you in reverse if that makes sense.
My solicitor has said to me the strongest points of my case and all of which increase my chances of a Judge ordering the sale are:
-He hasn't lived there the whole time since we split. He moved out and only moved back there recently. It's not been the children's "uninterrupted/habitual" home.
-There is enough equity in the property (not a lot about 20k) for it to be sold and for him to receive a a 50% share which enough to rehouse himself.
-Local rental prices are similar to the current monthly mortgage payments.
- I do not and will not earn enough to obtain a new mortgage whilst tied to the mortgage I have with him if I cannot sell.
-He claims he can pay the mortgage but has already underpaid it so it is in arrears. The charges being added on each month mean that he is increasing the debt which I am liable for.
-He isn't paying the (compulsory by the terms of the lease) monthly ground rent and hasn't since he moved in. Again, in joint names so he is accruing debt in my name and without sale I cannot stop this.
-Current repayments are interest only. With interest rates set to rise and given he can barely afford the current amount, he won't be able to afford the monthly payments. He has been irresponsible with the mortgage before and it could lead to debt/repossession- it's unfair to put me in such a financially vulnerable situation.
-He works and has a decent average wage. The Judge at our last hearing told him the fairest thing to do would be to buy me out.
-I took things to Court to force sale as a Tolata application, he hasn't yet made a Children's Act application to counter my claim, which I'm told he should be doing asap as the children live with him 50% of the time.
I hope some of the above helps you OP, in a round about kind of way, so you can see what you should be doing and shouldn't be doing now in order to put you in the best position possible for winning if your ex does make a Tolata claim to try and force sale of the property. X