If you keep just eating out every day, you'll start to miss home cooking.
Literal
Every-day eating-out only [with-で] settling are-doing [conditional-と], home-cooking [subject-が] come-to-miss.
ばかりで済ませる ('settle for nothing but') combines ばかり ('nothing but') with 済ませる ('get by with'). 恋しくなる uses i-adjective 恋しい ('longed for') + なる ('become'). 家族料理 is non-standard — the usual term is 家庭料理 ('home cooking') — suggesting this sentence is a translation.