So you were together. You had a shouty argument about her potentially cheating and she called the police and accused you of assault. Police arrested you and released you on bail with conditions not to contact her or go to the house pending further investigation. You went to stay with a friend. Police dropped the case and the bail conditions ended.
She has now changed the locks and refuses to let you see the children.
Is that a good summary? Have I left anything out?
If this is the case - I don’t think focusing on the locks or getting into the house is a good idea. Technically she shouldn’t change the locks and technically you can return to the house. But that’s just very obviously a bad idea. You’ve broken up. She’s accused you of assault. Living together is a bad idea. So even though you technically can go back, you shouldn’t.
You need to take her to court for a CAO so you can see your children. You can self-represent. Going to the house and letting yourself in when you no longer live there is not a sensible or reasonable way to see them.
You also need to start divorce proceedings and get an order to get the house sold if she won’t agree to a sale anyway. You could stop paying the mortgage, and insist she does in lieu of rent to you for “your” half of the house. But if she doesn’t pay it (and it sounds like she wouldn’t be able to?) it’s your credit that’s going to get dinged so might not be the best bet. A court order to allow you to get it sold sounds like a priority, some lawyers will wait for settlement before being paid, see if you can find one. Another alternative might be to release a bit of equity from the house or see if you can get a mortgage holiday, to pay your legal bills and get yourself set up to rent. Not sure how easy that would be with you no longer resident in the house, but since you have a lot of equity it might not be too difficult. If you do this, I would keep track of what you spend that money on so it isn’t seen as you trying to hide assets in court at a later date.