No, you can't. Sorry to be blunt, but if you don't trust your significant other 100% your relationship is doomed eventually. When you don't trust someone you can never be truly happy with that particular person and when you're not happy, you argue and fight. Eventually one person will get sick of the fighting and call it off. Can people change and learn to trust someone? Definitely. Is it hard? Absolutely. But, one person WILL have to change, you can count on that. Be it the untrusting person or the non-trusted person.

In the case of that 10 year marriage, obviously she still trusts him even though he a lapse in judgement. If she decided to stick it out with him after he cheated, she must trust him enough that he's not going to do it again. GL with whatever decision you make, relationships are tough.