My wife has alzheimers, and I'm her husband...

We both have medical problems... however I manage all her monies , i.e. checking accounts.

We both have separate checking accounts. I transfer money to my account to help pay out medical expemces.

This is her second marriage and I've been married before

Am I legally within my rights ?

How are you transferring funds? If you do not have a Power of Attorney and are signing her name or signing without her authorization you are committing fraud. If she has children, this could be a problem in the future.

Go to Court and have her declared incompetent and transfer money legally.

Yes how are you doing the funds transfers, you can not legally just take money from her account, ( that does not have your name on it) If you were added to the account, of it you were given power of attorney to do so.