Do you pay or receive the child support? It's a different affordability calculation.
Work history won't matter much, bank will only look at the last 12 months. They might look for evidence that savings weren't a loan from parents for example, but only if they appeared in your account recently.
Your problem is you're looking to borrow almost 5 times salary. So you'll need an exemption to LTI limits which seems to be what everyone is looking for at the moment, so the exemptions are in short supply, so some banks might decline and another accept. I don't normally recommend a broker, but might help in this case.
Keep up the consistent savings history. Even a small pay rise would help your case.