Yes the answer is a splitter on line one. Two line phones use jack one which has four pins active. Jack two only has two pins active and will only support one line. This is the way the modem is designed. Thus if you have two one line phones you can use jack one and two. If you have two line phones they have to use jack one.
If both phones are two-line phones, and the splitter is capable of splitting two lines (i.e. four wires / two pair), then yes, you could install the splitter in jack 1 and the 2 two-line phones into each outlet of the splitter.
Are you attempting to make use of existing house wiring at all?
If you are subscribed to 2 different phone numbers you should have a modem that
has multiple phone line ports. You would see Tel1 and Tel2. Tel1 would be assigned
one number Tel2 the other. If you have a phone that can have both phone cords from the
modem plugged in that would work.
If your telephones have only one phone line input you would need to have 2 different phones.
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If you dig up the manual or look at the back of the Arris modem you will see the first phone jack is labeled Tel 1/2 ( not Tel 1 ) and the second jack is labeled simply Tel 2. If you have a dual line phone ( a single phone that can support two lines) it will have one cable with four wires active, one pair for each line. I believe this is what the OP was describing. This phone would only work as a two line phone plugged into Tel 1/2. If plugged into Tel 2 he would only get line 2. If I understand the OP correctly he has two of these dual line phones he wants to use. Thus to get them both to work he would need a splitter for Tel 1/2 to plug them both in and get them both to support two lines. Also as another commenter mentioned it would have to be a dual line splitter, not a cheapie one from your local discount store.
This is is my reading of the original post. If I am wrong and the OP is still following he can clarify.