This would be a good idea to do anyway if your LLC is not filing it's own tax return. 

Your resident state CA will tax all of your income, including out-of-state gain.

Those that respond “$0” or something ridiculous, you can request income documentation from them to justify.Don’t be afraid to share with them how much your property taxes & Insurance increased and that YOU cannot afford to absorb them.ALWAYS get an increase or something of value annually or tenants will start thinking they should never have an increase, making future increases that much more difficult to negotiate.

There is no inheritance tax given the value of the estate.

My question is do I need to use all of the equity towards the down payment of the property, to avoid capital gains tax? 

There was an opportunity to help a fellow investor who had his family growing and needed to dispose of the property to get rid of problematic tenant issues, rising taxes, and invest in other opportunities closer to home.

Also make sure your tax basis is reduced as part of the sale since your land is being reduced. 

Never let the tax tail wag the dog.

You should look at any limitations on gift taxes though, and she may actually want to structure it around any of this.

I'd probably get into long term rentals for tax reasons.