Wealth - Bond Market and Liquidity Preference Framework
These are theories, so need empirical justification. They may not be true, and even if they appear to be true they may still be wrong about the cause and effect. 

If you regard your first statement as saying that people with increased monetary wealth will want to see a income increase from this wealth then they will buy bonds and other less liquid investments pushing interest rates down, and your second statement as saying that people with increased non-monetary wealth will want to see an increase in liquid assets such as money so they can spend some of their wealth then they will sell bonds and other less liquid investments pushing interest rates up, you will find there is no intrinsic contradiction. Instead you get an explanation of the existence of secondary markets in bonds and other investments to reconcile the needs and desires of different people