This might be a series of T-Bag... if a lot of time elapsed between the video being recorded and your watching it in 96-98. The long-running series finally ended in 1992!
The question is - which series? Different parts of your question point to different series as being the most likely.
SERIES 3:
The two children (they are a boy and a girl, but not brother and sister) differ between series. In series 3, we have Thomas and Debbie:
Note the paintings on the outside of that music box:
In each episode, the two children enter one of the paintings, and compete with each other to find one of a set of gold bells. Debbie is trying to save the inhabitants of the paintings from an evil witch, while Thomas has unfortunately been brainwashed by the witch and is trying to stop her.
For example, here's Debbie in a painting of a windmill in Holland - and the painted backdrop was VERY obvious on TV in the 1980s:
SERIES 4:
Now, you did remember the girl as being older than the boy. In series 4, Debbie is replaced with Holly, and she is noticeably taller than Thomas:
In this series, our two children were travelling between different television programmes, not paintings. But the obvious painted backgrounds were still there, so you might still have thought they were stepping into paintings. Here are the opening shots for a Dallas parody episode, and a Wild West episode:
SERIES 6:
Now, Series 6 wouldn't be as likely a candidate as the previous two - except that it's the only series to have a commercial VHS release! All the others would need someone to have recorded them for you using a home VCR.
The VHS release removed three of the episodes (including my favourite - a Sherlock Holmes parody). It also removed the opening credits for all but the first episode, and the closing credits for all but the last, creating the impression of a single story in seven acts.
The painted backgrounds were still present:
The evil witch in this series was not the witch of the previous series - but they both used saucers of magical tea to spy on their enemies:
Meanwhile, Debbie and Holly had now been replaced by Sally. Poor old Thomas was still being brainwashed into working for the bad guy - that young man could not catch a break!