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My mom can surely enter the US coz she has 10yrs visitors visa
She can seek entry, not the same thing.
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and my dad is currently petitioned thru an employer in the US. The question was, just in case my mom arrived the US using her tourist visa, and so happened the F4 got approved for processing(which is supposed to be in the Philippines) can she be allowed to stay and/or have the processing done and continue while she is in the US?
If she did not have this intent on entry, presumably this was filed many many years ago.
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And can my dad switch his ongoing employment petition into the F4 since he is already in the US?
Yes, assume he has a H visa?