Occupation orders are "free" to the extent that there is no Court fee payable to issue.
If you use a solicitor, and can't get legal aid, then you will have to pay the solicitor.
Your solicitor is right to advise the risk of a costs order against you if you are unsuccessful, since the rules for such applications are not the same as for other family proceedings, however, in my view, the risk is small, for these reasons:
You have findings against him of domestic abuse. The allegations were serious enough to warrant a fact finding. They included allegations, now proven, of abusive behaviour towards the children. Clearly, you and he cannot occupy the home together in a manner that protects the children.
He is in fact as I understand it excluding you from the house (locks changed). He is not allowed to do this. Even if the court won't exclude him, it should give you an order requiring him to let you back in, not interfere with your occupation further, and possibly forbidding him to use parts of the home, plus a non molestation order. This would be enough of a "win" to justify either no costs order, or him to pay your costs, imo. I don't think a judge will want to order costs aginst you, so they would be looking for justification not to.
Please remember your solicitor has to advise you defensively, so if it goes wrong you can't say you were misadvised. That's why we never give guarantees.