There is not one correct answer, any of the solutions below are acceptable but the OP might be persuaded by the number of hits Google reports.
Google News has 114 results for your and your children's
"Of the things he says that are wrong this is the most direct threat to your and your children's health."
Contact your legislative and congressional representatives and encourage them to support your and your children's right to privacy and push ...
For you and your children's Google News reports 323 hits
Grab your coat, hat and gloves, bundle up and head outside! Outdoor play is good for you and your children's health and physical development ...
How many babies born last year share you and your children's names?
Google reports 11,500 hits for your name and your partner's name
The account can be in your name and your partner’s name.
Simply enter the name of your team, your name, and your partner's name and you're all set!
51,600 hits for your and your partner's
- This thinking reinforces the establishment of a great deal of inaccurate thinking regarding the quality of your and your partner's ideas and choices.
- SimpleTax is designed to automatically maximize your and your partner's combined refunds.
and 339,000 hits for you and your partner's
- Complete you and your partner's taxable income details
- If you and your partner's interests are poles apart, you need to ask yourself whether you are willing to do the things you enjoy alone or with other friends.
Google seems to suggests that “you and your customers' interest” (if both parties have the same interest in common) or “interests” is the preferred solution.
It avoids repeating the possessive adjective your twice in the same sentence, and if the noun that follows you and your is plural, it is unlikely a reader will interpret joint ownership of the thing in possession. Compare:
- You / your and your partner's name = suggests that the couple might share the same name.
- You and your partner's names = suggests at least two names per person
You and your children's names = no ambiguity
Your name and your partner's name = unequivocal but repetitive. Possibly the ideal solution for government documents, tax forms etc.
In conclusion, if one is looking for a perfectly grammatical sentence and one which expresses clearly its meaning, then I suggest the following solution:
We have plenty of magic that will pique your interest and your customers' interest.
If one is looking for the most harmonious solution, without changing the word order or any of the terms being used then this is perfectly acceptable:
We have plenty of magic that will pique you and your customers' interest.