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Since this is an exception and not the rule, and this arises from a specific set of your mother's very own personal circumstances, it is unlikely someone else's experience will match this exactly, and in any case, there is no guarantee that someone else's outcome will be the same as yours. The best way to know the answer is a pragmatic one: try and apply, and see what happens.
If an appropriate explanation is given the next time she applies, I don't see why this would have a negative impact.1. If she doesn't travel now to uk before the expiry of her family permit, would that impact on her future family permit application?
Apply whenever you are sure when won't have to delay her trip again. As soon as she states expected travel dates on her application, I would think having a valid Family Permit or not at the time of application would make no difference since it will be clear the current permit won't cover the travel date, hence self-explaining why the second application.2. What is the best way to deal with this situation. Shall I submit another eu family permit Application now and give reference of her current family permit or wait for her current family permit expired then apply freshly application?