She’s looking forward to spend more time with her family over the holidays.

Correct sentence: She’s looking forward to spending more time with her family over the holidays.

• Use of Look forward:
- Looking forward এরপর to + verb + ing বসে।

Example:
- I am looking forward to receiving your letter.
- I am looking forward to seeing you.
- My friend is looking forward to going to London.

• বাক্যে mind, cannot help, could not help, with a view to, look forward to, be used to, get used to, worth ইত্যাদির পর কোনাে Verb আসলে উক্ত Verb - এর সাথে ing যুক্ত হয়।
যেমন:
- He came to Dhaka with a view to visiting a new place.
- Would you mind closing the door?
- I don't mind taking a cup of tea.
- He cannot help laughing out loud.

Source: Applied English Grammar and Composition, P.C. DAS.