We have 'parents day 어버이날' not 'mother's day'. it is May 8. Mother's day is 어머니의 날 if i translate in Korean.
Your sentences are like this in Korean
"행복한 어버이날! 엄마가 제 삶에 있다는 것은 정말 고마운 일이에요. 보살펴 주셔서 감사합니다.
Well. It's kind of difficult to translate it as it reads in English. but i tried to keep the original meaning and make it natural in Korean as well.