My mom is french so I would like a tattoo that says

My mothers love, eternity within.

Please don't search a translation off line... those always come out wrong.

I'm French and there are many ways to translate it. If you can explain me the personnal meaning of your sentence, I can help you.
For example:
"Ma mère, mon éternel amour" can be right but you can interprete it like you will love your mum for the eternity (maybe like you love your soulmate)

A small change "Ma mère, un amour éternel" mean you will always love her.

Mum = Maman
Mother = Mère