I don't want to use childcare as an excuse, but there will be/are many things I can't do.
I'd rather not use childcare as an excuse but because I have children, there are many things I can't do.
「育児を言い訳にしたくないけどできないことが多い」＝ I don't want to use childcare as an excuse, but there will be/are many things I can't do. / I'd rather not use childcare as an excuse but because I have children, there are many things I can't do.
ボキャブラリー
育児 ＝ childcare
言い訳 ＝ excuse
出来ない事が多い ＝ many things I can't do
don't want to / rather not ＝ したくない
I don’t want to use my child/children as an excuse, but there are a lot of things I can’t do while I’m taking care of them.
don’t want to use my child/children as an excuse, but there are a lot of things I can’t do while I’m taking care of them.
【訳】私の子ども／子どもたちを言い訳に使いたくはないけれど、彼らの面倒を看ている間はできないことが多い。
後半の文章は以下でもいいと思います。
but I can’t do a lot of things while taking care of them.
【訳】彼らの面倒を見ている間、たくさんのことが私はできない。
直訳で聞くと不自然ですが、英語の場合は I（自分）などの人を主語にする方がしっくりくることが多いです。
I don’t want to use 〜 as an excuse, but 〜＝「〜を言い訳に使いたくはないけれど〜」
I don’t want to make an excuse, but〜 ＝「言い訳したくないけれど、〜」
イギリス 
日本 
