Britney Spears is going strong with Paul Soliz, takes his children into the Inside Playground

Britney Spears is very back with her up-and-out bf Paul Soliz … because they enjoy family outings together … with some indoor pleasure.

TMZ obtained this photo from Britney in a black Mercedes Benz G-Wagon outside Lily Pad Playground in the San Fernando Valley … and people who tell us that she was rolling with Paul and two of his children.

We have been told that Britney, Paul and two children were rolled to the covered playground on Tuesday … with Paul Driving and Britney Riding Shotgun.

Our sources say it is the same car that Britney bought about a month before Paul in their relationship.

Britney’s appearance on a covered playground in the SFV came as a shock for other parents who saw their little ones who have a good time on Lily Pad Playground … but we told that everyone has let almost Britney be and not plague her.

However, there were some Britney interactions … We were told that she was heard that people were told inside: “These are not my children.”

When it was time to go, we were told that Britney paid the bill.

Britney and Paul have had a rocky way in public – including a Epic inflatable at the Chateau Marmont In May that almost landed Britney in the hospital – but Tuesday’s outing makes it clear that they are back in the saddle.

This is not the first time that Britney spent time with Paul’s children