During our era, on marriage a woman became as one with her husband legally and therefore any property she possessed would automatically become her husbands property, to do with as he wished.

Further that if no separate settlement granting her a right to her receive income from her own separate legal property during that marriage had been drawn up immediately prior to the marriage, then without any co-operation from her husband, Sir Thomas could not legally pass money to Julia without it becoming the property of Mr Yates.

But in this situation we, luckily, have a husband very desirous of pleasing his in-laws. Sir Thomas eventually found that

Julia’s match became a less desperate business than he had considered it at first. She was humble, and wishing to be forgiven; and Mr. Yates, desirous of being really received into the family, was disposed to look up to him and be guided. He was not very solid; but there was a hope of his becoming less trifling, of his being at least tolerably domestic and quiet; and at any rate, there was comfort in finding his estate rather more, and his debts much less, than he had feared, and in being consulted and treated as the friend best worth attending to. 
Chapter 48.

Sir Thomas therefore could influence and prevail on Mr Yates , to, at the very least, make a will favouring Julia on the event of Mr Yates’ death,and make provision for any future children in that will too.

There is also the possibility that Sir Thomas could improve their not so hopeless finances further ,and Mr Yates could set up a trust ,with trustees appointed to hold money separately form himself to benefit Julia.

Look at this summation of the law from The Complete English Lawyer or every Man His Own Lawyer originally published by Alexander Whellier.

The law considers husband and wife as one person; for the very being or legal existence of the woman is suspended during marriage, or at least is incorporated and consolidated into that of the husband , under whose wing, protection and cover, she performs everything and is therefore called a “femme covert”.

A man therefore cannot grant anything to his wife, but by the intervention of trustees, or enter into covenant with her; for the grant would be to suppose her separate existence 
page 290

To sum up , Mr Yates could accept money for Julia and their future children from Sir Thomas: execute a deed setting up trustees to hold the money for his wife, separate from himself and Julia could then receive the income. I would think the best people to appoint as trustees would be Tom and Edmund Bertram, Julia’s brothers.

Leaving Julia and their future children( if any) adequate provision in a will would solve any money problems for Julia on Mr Yates’ death.

Julia and Sir Thomas are very lucky in that Mr Yates is not a bad or avaricious person and is desirous to please his father in law. Had he been a Wickham, there is no way Julia would have had an assured financial position for the present of the future.