OP, i agree with you that 50/50 would be unwise in your circumstances. Your unpredictable working hours would make childcare very difficult. It sounds like their lives will be much happier with their mum and a clear routine.
So your options are to look for a job that's more conducive to parenthood and pursue 50/50, or accept that some of your salary must be paid in child maintenance even if that leaves you short.
Buying her out of the house seems like a bad idea. If you can't afford to pay rent somewhere, how will you pay the mortgage?
If you are saying that the mortgage is cheaper than paying rent for a similar house, and that you want the security of owning, then your ex will feel exactly the same and would be a fool to move out. Why would she? And why would you want to uproot the dc from their home, friends, school?
I suspect the only way that she will sell is if she can't afford to pay the mortgage. Or the building society does not allow her to take over the mortgage by herself.
If the building society doesn't allow you to remove your name, or the courts compel you to leave it on the mortgage, then you will struggle to get a mortgage anyway because it will be for a second home. Certainly the interest rates will be unfavourable.
It is heartbreaking when there isn't enough money to go around after a divorce. Very common for both parties to take a financial hit.