My moms lawyer said I am not entitled to see her will. Is this correct?

Yes and no. 
Yes in that unless and until there is a legal challenge, the lawyer does not--and indeed cannot--show you the will unless the executor tells him to (or provides the will to you himself): actual or potential heirs (children can be disinherited, so it's not automatic that you will inherit something) have no right to see the will, though the executor may, of course, show it to them. The lawyer works for the estate and therefore executor--you are not her client and so she can't divulge the will to you.
No, in that if you have a reasonable and good faith belief that you would inherit (which, as children, you would) but are not being told of any inheritance or provided a copy of the will to see for yourself what was left you, you could bring a legal action against the estate and executor for "an accounting"--to make the executor "account" for his actions and managment of the estate. In that lawsuit, you'll be able to see the will and the court can order the executor to follow it. This is your recourse as a potential heir if you believe you are being deliberately cheated of what you are entitled to or are being denied it through negligence. Unfortunately, you need to file the lawsuit before seeing the will, so you have to file before knowing if a suit is in fact justified.
If you want to explore a suit, contact a probate attorney.