I can't remember any title or author but I can remember that I was truly lost in the story and adventures! The teacher handed me the first one from a box that was a series, he said if you like knights and and dragons, you'll love this series. It was about a boy stuck at an aunt's or uncle's old dark dismal mansion and comes across a tapestry or painting that he looks at and gets lost in it and thinks that it's moving or the characters seem to have moved in their actions. Then one day he sees a spider on the outside end up inside, where he somehow falls in as well and befriends characters and has adventures and all sorts of crazy things.
I think you might be thinking of Castle Roogna, third book of the Xanth series by Piers Anthony.
Dor, son of Bink, is a 12-year-old magician and next in line to inherit the throne of Xanth. To teach him the skills he will need to rule the kingdom, King Trent sends him through the tapestry on a mission 800 years into Xanth's past to find the ancient and mysterious Zombie Master. Dor travels to the past via the magic tapestry of Castle Roogna and inhabits the body of an invading mundane barbarian. While in the past Dor is accompanied by a (not normally) giant spider named Jumper, who had been drawn into the tapestry with him, and meets his current governess Millie the ghost, a short time before her unfortunate demise. Dor must use his magic and every other resource he possesses to help beat back an invading wave of mundanes and find a way to restore Millie's zombie lover to life back in the present.Turns out the Zombie Master is Millies zombie lover and ends up providing the cure for his own curse.
It doesn't entirely match up, as he's intentionally sent into it, and the person who sends him through is not directly related to him (Dor is the son of Bink, who at one point defeated the "evil" King Trent before realizing that Trent wasn't all that bad and let him stay as king). However, it has the tapestry with moving figures, a boy sent into it, and the spider on the outside that goes in with him.