How can I get past this obvious lie? How can I ever trust the person I trusted the most again, if she continues to lie to me about something so fundamental?
You can't -- and you shouldn't. This is your HEALTH you're talking about here!
You should accept nothing short of 100% no-contact from her, full transparency, a full-panel STD test (with a copy of the results shown to YOU), and good MC/FT with a therapist trained in infidelity.
YOU need to decide what YOUR boundaries are, because the truth is, that -- over time -- we really do teach people how to treat us, and you've "taught" your wife that this is acceptable behavior. YOU need to begin to dramatically change the marital dynamic.
You may want to start with this:
Why are you cooking and cleaning, and buying beautiful things for a woman who is cheating on you??
"What is best for my kids is best for me"
Persevere = happily being patient over a long period of time