What would you like to ask?Does this make sense please correct me?

Question:

先週 月曜び は 七時半 車 で としょかん に 行けました。

I was aiming to say i went to a library last week monday at 7:30.............

But i think i got mixed up instead should it be like this

ともだち の おかあさん と

If i added that my mother went with me please help

Answer:

>i went to a library last week monday at 7:30.............

This does not say "by car" although your Japanese sentence is trying to say it.

Well, the correct one is,
先週の月曜、７時半に車で図書館に行きました。

>If i added that my mother went with me please help

ともだちのおかあさん means mother of your friend.

It should be 母と

Addition:
>so if i wanted it to be i went to the library last week on monday by car what would it be?

I included "by car" in my 1st answer.

>and for the mother thing if i got rid of friend and の could it make sense to go with my mother

What do you mean by get rid of friend and の? It's confusing because you talk about getting rid of English and Japanese at the same time.